Full range question

On a 98 outback there are 4 OEM stock speakers and 2 optional package front tweeters. the stock speakers are not coaxial and have no built in cross over to limit tweet frequencies. I think I messed up and installed a midrange woofer replacing a blown backdoor speaker.

https://www.amazon.com/Pyle-Woofer-....5+woofer&qid=1577730509&s=electronics&sr=1-2

This looks to be a component speaker being fed the full range of frequencies. Will this muddy midrange when it tries to play tweets? or Muddy tweets trying to play those? Should I install a 2 way crossover to block it from tweet frequency or is feeding it a full frequency ok since it's not as adept at playing the higher range frequency? Or is it ok attempting to force it into the role of a full range speaker since OEM car audio? The idea was mid range felt a bit lacking So I thought if I install a midrange woofer where I didnt notice a speaker had blown it would round out midrange and woofing above Sub. It's doing a solid job but Im thinking Im muddying everything not limiting it to it's frequency range.