One of the functions of the overflow tank is to remove air in the cooling system.

You just had your cooling system completely drained and it's likely that some air pockets got trapped when you refilled it.(think about all those small coolant passages in your engine)

The coolant expands when hot and you're seeing the air being purged by the circulating (expanded) coolant (through the highest point in the system) the hose that goes to your Coolant Overflow Reservoir.

Don't get me wrong, I think you're right to be concerned because having air in the cooling system isn't good. The liquid coolant absorbs engine heat and brings it to the radiator to be cooled. The air in the system doesn't absorb the engine heat.

Some vehicles are really hard to purge the air without using a Cooling System Vacuum Purge/Refill Kit.

Here's a video of a guy showing how to use one:

https://www.youtube.com/watch?v=KbQ77-zDOEo