Welcome!
You probably bought an EOS Rebel
T6i. (There's no such thing as a "6i"... but there are T6i, T6s, T6, 6D and 60D. All of them will be similar to below, except the full frame 6D doesn't have a built-in flash and would only do some of the things described with an accessory flash unit fitted to the hot shoe.)
Canon cameras "communicate" with off-camera flash by strobing the on-camera flash, which old-style optically trigger flashes might "see" and interpret as a flash going off and fire themselves too early. That might be what's happening. Make sure your built-in flash is not set to "Master" and trying to control other flashes off-camera. If you were instead using an accessory flash rather than the built-in pop-up, those use different types of communication... near-IR in some cases, or radio waves in the "R-series" flashes. IR or radio might not trigger the studio strobes, but you aren't out of the woods yet...
Another possibility, whenever the on-camera flash is set to ETTL mode, it will fire twice for each exposure. Before the shutter opens, it emits a low-power (1/64) flash that it uses to illuminate your subject and measure how much light will be needed for the "real" exposure, which comes a fraction of a second later and is synced with the opening of the shutter. Often that low-power initial flash will set off optically triggered, off-camera flashes, too early to sync up with the shutter opening. To prevent this, set the on-camera flash (either type: the pop-up built-in or an accessory flash fitted to the hot shoe) to Manual, rather than ETTL.
The most certain and safe way you could use those older flashes or strobes would be to get a set of radio transmitter and triggers. The transmitter fits into the hot shoe of your camera. Then you need a trigger at each of the off-camera strobes and will need to set their output manually.
Radio triggers will give really good range (probably more than you need, possibly up to 100 feet or more). They also don't require line-of-sight, the way optical triggering does.
Using radio triggers also nicely isolates your camera from possibly too-high trigger voltages of some older flashes and strobes. It was more of a problem with older Canon from the late 1990s and early 2000s, some of which were only able to handle 6 or 12 volts. Some of the 1970s and 1980s flashes triggered as high as 300 or 400 volts and could damage those cameras! More modern DSLRs are built to handle up to triggering at up to 250 volts, so are safe with all but the highest trigger voltage old flashes and strobes.
Actually T6i don't have a universal PC sync cord socket, such as is provided in many cameras for wired triggering of many studio strobes (usually plugged into a mini-RCA socket on the rear of the strobe). There are adapters that can be fitted to the hot shoe to provide a standard PC sync socket (the radio transmitter mentioned above may have one, too)... These may or may not isolate the camera from any excessive triggering voltage. I'd be cautious about using any of these. But there used to be a device called a Wein SafeSync that protected the camera from excessive voltage, while providing a PC sync socket via the hot shoe. I don't know if those are still being offered. (Note: "PC" in this case stands for "Prontor-Compur", two of the major shutter manufacturers of the past, who standardized this type of socket across most cameras, replacing several other earlier designs).
There will be no worries about frying your camera with excessive trigger voltage, if you use some sort of radio system. Those come in all sorts of prices. (Sorry, but the CamFi unit linked above is
not what you need... That's a remote camera controller, so that you can operate the camera wirelessly from a tablet or laptop... possibly even a smart phone.)
In fact, for simple studio strobe triggering, probably all you need are very basic radio units such as these:
http://www.ebay.com/itm/16CH-Wireless-Remote-FM-Radio-Flash-Speedlite-Trigger-w-2-5mm-4-Receivers-/311544737650?hash=item4889836f72:g:sj4AAOSwx-9Wuotg Or these:
https://www.amazon.com/Godox-Channels-RT-16-Transmitter-Kit/dp/B015CGESYK/ref=sr_1_3?s=electronics&ie=UTF8&qid=1485405992&sr=1-3&keywords=radio+triggerI haven't used either of those particular systems (and there are
many different ones), so really can't say how well they are made or work. This is just for reference as to the
type of radio transmitter and receiver you most likely need. All these do is fire the strobe. They don't have any means of other control such as adjusting the output remotely. In other words, they have no "ETTL" functionality (which might be wanted if using modern flash ETTL capable off-camera). But this should be okay since those strobe units are probably not ETTL or any other type of remote control, either. Most studio strobes have an optical trigger, as yours appear to... but those will be fired by anything resembling a flash going off, as described above. They also are a royal pain if anyone else is shooting nearby with flash!
Radio triggers are the solution. Both the above examples are 16-channel, too.... so can be set to a different frequency than other radio triggers being used nearby, if that ever occurs.
One last thing... Many studio strobes do not reach peak output as fast as portable flash. So very likely you'll need to use slightly slower than the standard flash sync speed of the camera (1/200). Experiment with 1/160 and 1/125. (Obviously, you also won't be able to High Speed Sync or Rear Curtain Sync with studio strobes. Those are only available with dedicated portable flash and a few of the most advanced modern strobes.)