It seems like the pages should be redirecting based on the code that I can see in them. If the insert and updates are occurring correctly the code for the redirect should execute and take you to the details page.
It may be worth trying to add in an exit after the header. It is not very common but I have seen before where not having this in place after the header caused the location not to be updated.
The line of code appears near line 83 on the insert page and near line 101 on the update page. Here is what you should update it to:
Please give this a try and let us know how it works for you.