All A-B PLCs scan the user code from top to bottom, as do the majority of other PLCs.
An output instruction eg. OTE --( )-- is just an instruction to the processor to write the current logic state of the rung to the memory address specified, and it will do that as and when it encounters each instruction.
If an output bit is used multiple times, then it could be written on, off, off, on, etc. several times during one processor scan.
A-B PLC5's have "Synchronous I/O". That means the Output Image data-table is written out to the output modules between logic scans, and in this case, the "last one wins" rule will apply.
However, some A-B PLCs, for example the PLC5/250 (Pyramid Integrator), and the ControlLogix series, have "Asynchronous I/O", where the outputs are transferred to the output modules at a time that is not synchronised to the logic scan at all. In this case, the "last one wins" rule cannot apply, and the state of the output will be determined by which rung was execuited last, not the last rung in the program.
However, that said, digging deeper into your post, you said the outputs in question were N-file bits, which of course are not outputs at all, just memory locations.
I imagine that at some point the N-file data is copied to the O-file to set the state of the TTL outputs.
If this data transfer only occurs once in the scan, then the physical output data will not be going on and off, but will be set only once.
The source data may have changed many times during the logic scan, but the output file data will be static.
And then I read that you have several JMP/LBL instructions in the program, and I can also imagine that the programmer may have organised this code so that only one of the sections of code is executed, thereby enabling only one write of the output data.
This could have been done to reduce scan time, for example, but using JMPs and LBLs to do this is, in my opinion, sloppy programming. There are better ways to organise code execution.