It seems to me that there is a bug when a province is captured: if a move order had already been issued, the travel time doesn't seem to change.

For example, when I capture a province and the opponent has already given a move order for some of his units towards it, the units' travelling time doesn't seem to change, despite the fact that they now have to travel in enemy land (-50%). Same applies to my units as well: if I give them an order to capture two provinces in a row, the movement speed doesn't appear to change after the capture of the first province.

Well, in programming it is called a bug. The reason is that I CAN MAKE my units move faster (by giving again the move order), while the opponent cannot slow down my units after capturing my province.

(For those who don't know it, a well-known joke between programmers is to baptize "features" the bugs of a program).

That, of course, is always the designers' choice, and it should always be respected (it is their rules) - no matter whether is goes against the supposed function of movement factors.

Perhaps, in the players' tips there could then be added something like the following:

Better not to give move orders that extend to more than one territories, in order to save time. You don't want your troops to move with -50% speed even after you have captured a province.

Given the quite a few complains of the new players (mainly in the chat) for the speed of the game, it would certainly be nice to get rid of unnecessary delays.

No, if it was then you wouldn't be able to adjust manually by giving again the move order.

I can understand a valid reason why (it would require an event trigger every time a province is captured, which might slow down the game). That is acceptable reason - but then it is better that players are warned about this behavior.