Regardless of the type of reel (level wind, spinning or fly reel) it always important to watch how the line is going onto the reel whether fighting a fish or quickly reeling in to re-rig or cast. Reeling in a tangle onto the reel while playing a substantial fish is a possible disaster.
Normally, I would use my right hand fingers to tuck the fly line, above the tangle, behind my forefinger/middle finger and against the cork. From there I would attempt to use my off hand to untangle the mess by allowing some slack to the line around the tangle. If the fish is sizable, you may only get one shot at this. In the photo above, I never noticed the tangle as I fought the fish.