From the Thresh wiki page:
On Summoner's Rift, the drop rate for souls from small minions is 33%. However, the probability adjusts dynamically. If you are above or below your expected quota of soul drops from small minions, the probability lowers or rises by a small amount until you are back at your quota of drops. It is worth stressing that this only takes into account souls dropped, and not souls collected.
Nothing else effects the soul drop rate, though you can get them from jungle camps and enemy champion deaths. Landing the killing blow has no effect on whether a soul is dropped.
In practice, this means each wave drops 2 souls on average plus one for each cannon minion (every third wave).
Since the first wave spawns at 1:30, and a new wave comes every 30 seconds thereafter, by 10 minutes there will have been 18 waves spawned. Practically, it takes minions 30-35 seconds to reach the middle of bottom lane. This means you'll just be seeing the 17th wave at 10 mins and the 18th will have just spawned (assuming you aren't farming behind their towers).
So, 16 actual waves have died. That's 5 cannon minions, and 2 souls per lane otherwise on average, for a total of 37 souls at 10 minutes.