This topic is worthy of discussion and we can all benefit from having our awareness of it increased. Where overall tint is concerned, there can be several causes and there are therefore several different solutions.

Your posted shots are an example of the limitations attached to using just one technique. You obviously moved the Tint slider away from green and towards magenta. The result is an unwanted magenta tint that shows up in specific areas. The problem is, it's not just a green/magenta problem. I suspect the problem is it's more of a yellow/green tint in the foliage probably caused by the strongly yellow ambient light. You would probably have achieved better results if you'd included a WB adjustment because that's designed to work when it's a yellow/blue problem. You were trying to deal with a yellow/green problem with a tool that corrects green/magenta problems, and as a consequence you overdid the move towards magenta. If you'd included a WB shift away from yellow you would have needed a less extreme Tint shift.

The other main technique for dealing with tints is the HSL tool. You would have found that yellow and green were main players in the overall colour cast, and tint-shifting and desaturating both yellow and green would have gone a long way towards normalising the colour cast.

That raises the question of ambient light and whether or not you want to mess with it. Ambient light typically produces an overall colour cast that affects most things in the scene regardless of their colour. We see the effects of ambient light all the time and our brains are well accustomed to correcting its effects. But even then, it's very often the case that an ambient tint is what makes a scene interesting, atmospheric or just pleasant to look at. In such cases, if you were to remove the ambient tint you would be removing the very thing that made the shot special and worth capturing in the first place. Normalisation is a process that can be inappropriate in many cases and it's also very easy to take it too far. That is especially true of tints due to ambient light.

I would say that your posted shots are an example of how ambient light can make a shot too garish - which IMO is usually an undesirable effect, although there may be times when that's what you want (for example if you want to emphasise bright sunshine). In such cases where some colours (for example the green/yellow of grass or foliage) are being represented too strongly, the usual culprit is yellow light. In the above example I suspect that the camera was also a player in that it rendered the colours with too much of a green bias, hence the need for a shift towards magenta.....

......Which reminds us of the other main source of colour casts - the camera itself. The camera's influence includes how its raw data from the sensor is interpreted, and as has been shown elsewhere, all cameras aren't equal in that respect. So we can't assume that what we're getting from the camera (even in a raw file) is perfect or optimum.

And because it's a problem that often has more than one cause, it often requires more than one technique to deal with it.

The answer, as suggested elsewhere, is to be "conizant" (I would spell that "cognisant" ) and to be familiar with all of the correction tools (the main ones being WB, Tint and HSL).