Thank you for your post.
When you commit and flush the results, your cursor is not active in any field. Therefore, you need to capture the portal record (row) before committing and flushing so you can then return to the same portal record and go to the next field. To do this, your script may look something like:
Set Variable [ $PortalRow ; Value: Get ( ActivePortalRowNumber ) ]
Commit Records/Requests 
Flush Cache to Disk
Go to Portal Row [ Select ; No dialog ; $PortalRow ]
Go to Field [ <next field in portal row> ]
In step #4, after selecting the same portal row that you left, then select the next field. Since the OnObjectModify script trigger occurs before the tab to the next field, you don't want to select the next field and then tab out of it when the script trigger finishes. By placing the Halt Script at the end stops the ending tab from executing.
Let me know if you need additional clarification.
Why does the it go to the first record, activate and select with FM Go and with FM Pro it does not go to the first record, activate, and select the field?
If this difference occurred between Window and Mac when using FM Pro what would be done?
The expectation is that it would be the same experience on BOTH platforms.
Not a consistent experience, I should not have to worry about this nuisance.
Have a great day!
FileMaker Pro will also be similar. That is, if you commit the record, the cursor is not in any field, so if you go to the next field, it will select the first row in the portal. There is something you left out in the description of your script.
FileMaker Pro will not automatically jump to the next field when a value is selected in a field formatted as a Pop-up menu. FileMaker Go will automatically jump to the next field when a value is selected in a field formatted as a Pop-up menu. The script basics I showed above will work for these differences in both FileMaker Pro and FileMaker Go.
Ok so maybe it does not got to the next field in Pro BUT it does not go to the top record and select in Pro.
When it does this in Go and the first record is not shown it will go to the top record requiring the user to scroll through the portal, this does not occur in Pro.
Therefore the different experience.
Have a great day!