I'm sorry but "I'd imagine>>>he would have told me to go around" does not apply.
You are in a situation of false security, for want of a better description.
You really must talk to your instructor about what the "controller" is authorised to do.
Crash One is right with this.
The decision ultimately lies with the pilot in command.
If it feels dodgy, don't wait to be told. You're the one whose life may be on the line, and the 'controller' doesn't have a giant fishing rod waiting to pluck you out of the sky if it all goes tits up.
Also, regarding learning RT - it's worth getting classroom based training on procedures and calls using real world examples. Learn the WHY as well as the HOW & the pieces will fall into place.