Take a look at the info in "Setting up Script Triggers" in FileMaker Help.
Some triggers, such as OnObjectModify, are tripped after FileMaker processes the event that tripped the trigger. Others, such as OnObjectValidate and OnObjectSave, process the event after the script performed by the trigger is performed. Thus, the user presses a key or clicks the mouse to exit the field, the script is performed that puts the cursor into the desired field, but then the mouse click or keystroke event is processed and the focus changes to the clicked object or the next field in your layout's tab order.
To keep FileMaker from processing the triggering event, add an Exit Script [False] Step to the end of your script to cancel out the triggering event.
Thanks! That fixed it. To clarify for any others that encounter this: after the Go to Field step in the script, add an Exit Script step and enter "False" as the script result. It will show as Exit Script[Result: "False"]