This one is a bit tricky since as far as I know there is no such piece of information in the backup header.
I used this process to do it. (solaris to linux. version 15.0.3) Not recently so don't have the script but I am sure this was it.
1) Kill and lock all the users in the database.
2) Make the database single user mode
3) dump the transaction log.
4) sp_flushstats and then wait for few seconds for everything to become quiet.
6) checkpoint to clean up a bit.
7) dump database here
8.) don't forget you put the db in single user mode and locked the users.
It has worked for me consistently but I have read else where (this is hearsay..) that it used to be inconsistent because of garbage collection or checkpoint kicking in during dump process.
Couple of suggestions
1. I think one option for you may be encapsulate the whole thing in a script, pass it to customer and request the script output from the customer along with the backups. At least this way you know what exactly was done.
2. If that is not possible then probably you may have to use the staging server as a part of your load process and in corporate that time in your ETA's. Still frustrating but at least you can plan your coffee break better. 
warm regards,
sudhir