I don't know what it could be other than a css compatibility issue as I have not done anything other than download and activate the plugins (types, views, layouts). So, I can only assume that it is a bootstrap thing.
As you can see from the shared images, there is a space of about 100 pixels that gets shifted up.
There is also a modal that pops up, usually the background has a dark overlay, but when toolset is active it, there is nothing.
Link to a page where the issue can be seen: hidden link
The short answer here is that Toolset does not yet support Bootstrap 4 and is only tested and confirmed compatible with Toolset 3.
A colleague has tested Bootstrap 4 with Toolset on his own sites and has found that it pretty-much works as expected.
We will formally test Bootstrap 4 and make any required changes—I don't know when exactly—but in the meantime it is a question of identifying any specific issues as they arise and providing ad-hoc CSS overrides as required.
I can't see the issue at the link you shared, you are presumably using Bootstrap 3 (or have Toolset disabled).
Using the browser dev tools it should be fairly straightforward to identify what causes the content to shift up so as to add a style rule that fixes it.
If you need help with that can you create a comparison page where I can see the issue so that I can compare it to the current page which displays correctly?
I'm finished for the day, but let me just quickly answer that last question.
Toolset depends on Bootstrap for the Layouts grid system, everything else is pretty much optional (it means having some default styling for form elements, and you can output Views with Bootstrap markup).
You can go to Toolset > Settings and specify that Bootstrap is not being used on the site, meaning Bootstrap CSS and JS will not be loaded by Toolset. The only thing that will actually break should be the Layouts grid, which would only be a problem if you are using it.