You're being entirely rational.
Putting milk in first increases the viscosity of the liquid you're trying to get through the "bag," making it harder - and taking longer - to infuse to the desired strength.
( argyleblanket The man on the roof works for me, Thu 31 Mar 2011, 20:00, 1 reply)

Critically..
... it also makes it colder and very hot water is required to make anything resembling decent tea. The critical components are simply not extracted effectively unless it's very nearly boiling. Sadly, that means that if you add the milk in shortly after then it will scold the milk. However, if you leave it to cool then it will separate because the milk stabilises the tannins, which are not very soluble.

So you can have:

Milk then teabag then water - insipid nastyness

Tea then water then milk - tea but tasting a little off (scolded milk)

Tea then water, remove tea and allow to cool, add milk - separates unless you have perfect timing.

Use a teapot & add the milk to the cups - actual real tea. Yay!
( Ugi , it's a game of give and cake, Fri 1 Apr 2011, 10:49, closed)

Scolded milk
No! Bad milk! Up to your room and no tea for you!

Edit: spot on in your analysis of what order to do things in though. Brew up in a teapot and put milk in the cup first!
(flimflam_machine, Tue 5 Apr 2011, 16:31, closed)