Hmm. If you have two hots connected and they are connected to the same buss bar in the service panel, then the result will be... 120V. You could end up with more amperage on the neutral or neutrals than the circuit breakers are rated for, though. A picture might really help, here. If the hot wires come from different buss bars, you'll have 240V on the wire because that's the total potential from one pole to the other on the transformer outside your place. The voltage won't hurt the wire, but it could cook connected equipment. Plus, you'll also have a direct short resulting in lots of amperage, so it should trip the breakers and nothing would work at all.
It sounds like if indeed you have hot wires from two different branch circuits connected together, they are on the same leg (same buss bar). The easiest way to see which one goes to which breaker is probably to undo the wire nut, flip breakers off and use an electrical tester to see which breaker cuts the power in which wire. If they're disconnected from one another, each wire should be energized at 120V.
While it is conceivable that an electrician made a mistake, I wouldn't hesitate to call in an electrician on that basis. Licensed electricians are professionals, by and large in both name and practice, who have had enough training and hands-on experience working as a journeyman for a licensed electrician to qualify for their professional license, plus the subsequent experience and continuing electrical education as a licensed professional. If you're worried about one particular electrician, call a different one.
If the one you think screwed up is a personal friend and you're worried about hurting their feelings or not getting invited to the next wedding, then call in the "replacement" when the original guy is really unlikely to just stop by, like during the middle of the day when both electricians are likely to be busy with business. :-)
On the old receptacle were the break-off tabs connecting the contacts on the hot side of the two receptacles removed? What about the break-off tab on the neutral side--was it removed or in place? If you just want to use only one hot (red or black) to power both receptacles of the the duplex receptacle, then on the new receptacle, don't break off either of these connecting tabs.
But if you would want to power the two receptacles independently using one neutral (i.e., a MultiWire Branch Circuit (MWBC) using both red and black and the one white), you must put in a 2-pole breaker and put it in a different spot than this tandem breaker. This might require rearranging the breakers in your panel. If you would try to insert a 2-pole breaker in the same location as this tandem breaker, I believe you would find that the 2-pole would not snap into place. It is that way on my GE panel and I think this is a universal requirement.
And on the new receptacle you would remove the break-off connecting tab on the hot side, but leave the tab on the neutral side intact. (You have only one neutral and you want it to serve both receptacles.
In any case do not connect the red and black wires together. You either abandon one of the hots and cap it or, if you use a MWBC, you connect each hot to "its own" receptacle.
Best Answer
To make it a little clearer tandem breakers are on the same leg. MWBC are on opposite legs. Voltage measurements on tandem hot to hot the voltage is 0. The voltage on MWBC hot to hot is 240v.