Is it okay two breakers are controlling the same outlets and appliances?
Probably. Here's a diagram of how a main panel and a subpanel are usually wired together:



In this diagram:


The main panel (on the left) has one breaker at the bottom that controls two outlets.
The subpanel on the right gets its power from the top right two breakers in the main panel.


Turning that pair of breakers off will turn off the entire subpanel.

The subpanel has one breaker that controls three outlets.


So if this behavior matches up with what you are experiencing when flipping breakers, then you're probably OK. Obviously there will be slight differences, such your breakers will probably not be in the same positions in my example, the pair of breakers in your main panel might just be one double-wide breaker, or (unlikely) the pair of breakers in your main panel might just be a single breaker.

But if you're concerned, it is worth it to pay a second electrical contractor to come out and look over the other guy's work. Also, the work should have required permits and therefore an inspection by a government inspector. If that didn't happen, then that might be a red flag.

Also, new electrical work like this must be labeled properly to meet code in most jurisdictions. You are will within your right to call the electrician and insist he properly label his work.