I couldn't find any answers on how to use/implement Google Content Experiments with GTM.
I currently have set-up a GTM container with GA code and in the original page for the experiment i have the Google Experiment Code at the beginning of the html tag. The problem I'm having is that not all users are counted in Google Analytics Experiments Report.
It's still impossible to implement Google Experiments with GTM.
However as far as I understand - you implemented the experiment code in the normal way. Did you checked if the experiment is set for 100% of your visitors? If it's less - it's normal to get some visits outside of the experiment and it sounds like this is the case with you.
Other than that - the GTM shouldn't affect the experiment itself in any way, as you don't use GTM for it.