Charlie's turn is interrupted for as long as Tim is taking his Time Stop turns.
Time Stop states:
You briefly stop the flow of time for everyone but yourself. No time passes for other creatures, while you take 1d4 + 1 turns in a row, during which you can use actions and move as normal. [...]
If Tim interrupts Charlie's turn with his readied Time Stop (note the rules on reactions interrupting their triggers; in this case, Tim has to wait for the trigger to finish), he simply (if that's the appropriate term here) stops time for everyone but himself.
When Time Stop ends (because the turns are over or Tim affected someone else), both Charlie's turn and the regular initiative order resume.
Overall, whether you're Time-Stopping or simply using a regular Readied Action to smack Gary the goblin on the head, the result is the same - the current creature's turn is interrupted, you do your thing, and then the creature's turn resumes. Time Stop simply allows you to do more during the interruption.
tl;dr: Nothing in the spell states that it only works on your turn, therefore it also works during Charlie's turn. It also doesn't end Charlie's turn, as it doesn't say that it does.