if he put a roller lifter in sideways, it would be destroyed seconds after the engine ran and he would have more than backfiring. like anything roller lifters will have a wear pattern to their cam lobe but to mix roller lifters is really not a big deal it certainly would not cause a problem immediately... maybe after 50k miles. if it had flat tappet lifters (i seriously doubt it but i don't know saturns) then those do wear into their respective cam lobes and a flat tappet lifter spins in it's bore as it rides the cam lobe based on a slight angle on the bottom of the lifter. when you mix flat tappet lifters to different cam lobes that normal spinning operation is upset and there's a high risk of the flat tappet lifter not spinning and wearing out the cam lobe.
i don't know saturns but my best guess is you have lifter preload wrong and the valve is not opening all the way or is hanging open, if the valve does not close and seat that will certainly cause backfiring. i would first undo the rocker arm on both intake and exhaust valve then pressurize the cylinder with air and verify both valves fully close and seat on their own and that you don't have a worn valve or valve seat.
then connect one rocker at a time and rotate engine observing valve operation making sure it fully opens and closes. I don't know saturn but you either have adjustable rockers or you don't. if you don't, then all you do is tighten down the rocker fully it's the length of the pushrod and the pedestal height of the rocker when tightened down that fixes your lifter preload, the rocker gets tightened with the lifter on the base circle of the cam where the lifter touches no part of the cam lobe, if it does then you have the possibility of offsetting the rocket and binding it when tightening down because you're going against valve spring pressure. if you have adjustable rockers, then you must have lifter on base circle of the cam and how far you tighten down the rocker nut determines preload and most likely where your problem is. a quick way to tell is on another cylinder you have not touched is see if you can tightened down it's rocker another 1/4 turn, if you can you have adjustable rockers, undo that 1/4 turn obviously and put that lifter preload back to where it's supposed to be.
and you do not have to soak or fill hydraulic lifters with oil. they fill immediately after oil pressure gets over 1 psi after the engine starts. at most you coat the outside of the lifter so it isn't dry and score the lifter bore when it first moves during engine cranking.
