"Al rato mismo"
I hear this all the time at work. I think they are trying to say "In a little while" or "after a while" when they say it. It seems like it would mean "At the same time" but I don't think it's used like that. Anyone hear this?
I usually say "Al rato" meaning "some minutes later"
Ex. Le dijo que no iría y al rato apareció
The noun "el rato" pops up in many time-related phrases; it can mean "while" or "moment." I've seen 'al poco rato' and even just 'al rato' used to mean 'in/after awhile, soon", etc.
As you mentioned, 'mismo' can indeed mean 'same', but it's one of those tricky modifiers that changes meaning based on it's position relative to its noun. If it precedes its noun, then it means 'same' [el mismo coche = the same car].
However, if it follows its noun, it can mean something like "per se, in itself/oneself," and in many phrases can express 'right, just,' etc. For example: ahora mismo = right now; ayer mismo = just yesterday. So perhaps the phrase you're hearing means something like 'in just awhile.'
I've heard dentro un rato which I take to mean "...in a little while" as in
vamos al bar dentro un rato "we'll go to the bar in a little while"