Benzos and antidepressants are often prescribed together. They were for me. And are. So don't worry about that part.
There shouldn't be any concern with taking the two medications concurrently. Actually, it would not be advised to cut your Klonopin taper short and stop taking that abruptly, as benzodiazepine withdrawal can be dangerous.
Definitely give your doc a call to clarify that he wants you to start the citalopram right away, but my guess is, that's what his plan was.
Keep in touch!