I think the temperature and feeding schedule are the culprits.
If you're using equal weights of flour and water, then you're using
what many people would call a "liquid" starter. (I use twice as much
flour as water to produce a "firm" starter. Either is fine.
I wouldn't say that liquid starters become "foamy," but they do
develop visible surface bubbles at the end of their growth phase,
i.e., just before feeding.
However, your starter is not going to grow properly at refrigerator
temperatures. The refrigerator is only for long-term storage.
What I do is go through a few refresh (i.e., feed)-and-grow cycles at
room temperature and then store it in the fridge for a few weeks.
Then I take it out of the refrigerator and repeat.
Finally, you're probably including way too much starter with each
refreshment cycle. If you are doing two room temperature feedings a
day (1 every 12 hours), then try using equal weights flour & water,
and then 1/3 that weight of starter.
Allen
SHB
San Francisco