File Maker Pro 9 on iMac OS X
I do this type of thing all the time in filemaker. There are details missing from your post that are key to exactly which approach will work for you.
" When I select the Order ID that I want to work on in the Pull-down, the Tab control jumps to that record set associated with it."
How have you set up your tab control? Just as you can't give an MS Access tab control a record set, you can't refer a tab control to different "found sets" of records in Filemaker. You can put a portal on your tab control that will function very similar to a sub Form in Access. Is that what you had in mind? It can be done fairly easily with a filtered portal.
"...3 Pop-ups that each filter down to the next Pop-up. "
This is called a conditional value list in filemaker terminology. You can research those keywords here in this forum. (Click the Advanced link above.) You can also check out the following link to a thread that walks you through the process: