That is, in fact, quite contrary to my experience. I had a trade route with the Ottomans in my GB campaign, and every turn I'd have to watch a dozen plus 3-4 ship fleets move around the Adriatic/Aegean Seas. I also saw a whole bunch of small troop movements up through the coast of Greece.

What you seem to be describing is basically what I see currently in India in my UP campaign. I've purchased Bengal and the coast province below it from the Mughals, purchased Carnatica from the Maratha and Goa from the Portuguese, conquered Mysore and Gujarat once it went rebel but traded it to Britain. The Maratha still have Hyderabad, Bijapur, the province between Bijapur and Gujarat, and one north of there between Hyderabad and Hindustan. Aside from a small 4-unit raiding force the Maratha have flitting around in border territory, neither one is moving at all. The Mughals have a full stack in Punjab, a full stack in Hindustan, and a full stack sitting in a rice estate next to Hindustan!

The Maratha have a full stack in Bijapur and a full stack in Hyderabad, but other than a few ships and the aforementioned raiding force, I haven't seen a single troop movement from either of them in years. They just won't move.