I concur about the marks being drying marks, but not with some of the advice given. Too much hearsay, misinformation and speculation.
Whatever wetting agent you use (Photo Flo or Edwal, etc.), it's function is to break up the surface tension of water, preventing the formation of droplets. Proper dilution of the surfactant ensures this is accomplished without leaving excess surfactant around to make marks on your film. Use the manufacturers' recommended dilution or a little weaker, if a weaker dilution sheets well and prevents formation of droplets (this is an easy visual check).
If your water has dissolved minerals in it, you need to get these out of the emulsion before or during your final rinse with the wetting agent. Distilled water is your friend. Soak the film in distilled water for several minutes (3-5 is my preference) to ensure that the level of dissolved minerals in the emulsion is low enough not to cause deposits on the film when dry. The more mineral-laden your water, the longer you'll need to soak. Don't reuse this bath for more that a session (or less if you've got a lot of film per session).
FWIW, I use a distilled water/wetting agent solution for my final rinse. I leave the film in for five minutes or more, with gentle agitation. I have never, in more that 30 years, experienced a problem attributable to letting "the film just sit in any surfactant for a long time." Film is just emulsion on a waterproof base; in 30 seconds or so, the emulsion is saturated with whatever solution in happens to be in contact with. A longer time in the solution then makes no difference regarding the amount of chemistry present in the emulsion itself. However, if there are dissolved minerals, etc. in the emulsion from earlier solutions mixed with tap water, they will leach out into a solution with fewer or no dissolved minerals.
There seems to be a general reluctance to squeegee film here. Shaking, spinning or doing nothing whatsoever seem to be preferred. Certainly, if you've mixed your wetting agent correctly, it should sheet up and run off the film by itself over time. That said, puddles of wetting agent can accumulate around sprocket holes and on film edges (and on the film surface if you've not got a correct dilution of surfactant) causing accumulation of the surfactant itself after the water evaporates and thereby leaving marks/spots/streaks. When I shot roll film, a gentle squeegee between two clean fingers dipped into the wetting agent first removed excess liquid, prevented marks and sped drying. With 4x5 sheet film, I use two swipes between two fingers. Prints get a quick squeegee with a (new and clean) windshield wiper blade. Never a scratch. Film processing machines have squeegees built in that work just fine when clean; why is it that we are hesitant to squeegee our own film then?
I recommend that the OP do the following (since the film is on plastic reels): Use a penultimate distilled/demineralized water bath where the film sits and soaks for 3-5 minutes. Then remove the film from the reels and gently see-saw it through a deep tray of wetting agent (mixed with distilled water and at the proper dilution), taking care not the scratch the film on the tray. After 30 seconds or so of this, squeegee the film gently between two wet fingers along its entire length with one swipe. Hang to dry in a dust free place. With stainless steel reels I simply put the film on the reel in the wetting agent. Plastic reels seem to have some issues with film contact and with residue, hence the suggestion to remove the film from the reel.
Best,
Doremus