If You need to clear immigration/customs, come inside, collect bags & give back to next airline, you will be coming in to Schemgen area.
I assume all of these legs are on seperate tickets as most of the time on a single ticket you dont need to collect & re-check in the bags.
So, yes, as you are coming to land side, you need transit visa. You would not have needed it in case airlines were going to transfer your luggage on their own, know as TWOV(Transit Without Visa), not available to 10-11 nationalities (India is not there, Pakistam, Afghanistan, Sudan & Few more, Philli definitely not there).
The other option will be to travel without check in luggage, but I think boarding passes for Air Europa leg will be the problem. ( Edit: as stated in comments, this does not apply to OP's current flight schedule, as there is journey from rome to madrid.)
Plug all of your data, like nationality, embarking place, transit, destination etc in Timatic Web system ( the same what many airlines use, and provide free access to travellers) at KLM. Google travel visa timatic, Emirates provides, few more also do.
Note that in timatic, transit means you are staying airside.
Edit:as confirmed by @phoog in comments below, the rome to madrid will be essentially a intra-schengen flight, so luggage or no luggage, you need a visa; or change of ticket/route.