but when I go to its activity the old cost is still used to calculate the rest and revised costs
No, that's not possible.
The cost of the function is calculated on the current date and is applied to the real, the left and the revised costs.
Only the cost on the assigned remains unchanged and on your capture we only see the assigned starting cost.
This allows you to compare the variances on the costs assigned at the start of the project with the new costs.
On the first capture you can see the cost calculation on the "support A" resource, estimated at 20 € / d, and planned over 10 days with 3 actual days until the current date.
So the real cost is 3 x 20 = 60
I change the cost of its function for 55 € / day from the 5th
You will notice that the assigned cost have not been changed. This is the starting assignment.
On the other hand, the real, the rest and the revised are well updated with the new prices
The actual cost = (2 x 20) + (1 x 55) = 95
It is about life. It was estimated X months ago that our resources would cost us (10 x 20) 200 euros for this activity and today, with the contingencies (absences, standby of the activity, evolution of costs, salary increase, .. .) it will cost you 480 €.
- it is possible to modify the tool so that this situation is taken into account each time a new TJ is recorded. Because it is a situation that can also happen during the year
So no, since the modifications are taken into account.