Is it possible to get a slow leak straight after installing new tires?
I would more suspect a leaking valve. 
If you pinch the tube putting it in then it is typically not a slow leak.

If the valve is removable the pull it and look for any debris or defect on the seat. 
I had a set of cheap tubes that had like 1/2 loose valves. 
Remove it with pressure in the tire to blow out debris you cannot get to.