Publishing multiple iOS apps using different developer accounts
Does Apple monitors what apps upload from the same Mac?


No.


  Can I run into any troubles?


No.


  Does this interfere with apps review?


No.

You should be absolutely fine given that you have proper distribution certificates setup for both the accounts and you use the correct ones while creating the app archive and publishing them.

Publishing apps for different account is a routine activity performed by freelancers and companies engaged in offering bespoke iOS development services.