Got 2 different "security code" emails I didn't ask for. What's going on? Is my account compromised?

I am glad to say that Thomas from Advanced Support was extremely MVP and emailed me back with a clear reply. Just in case this helps anyone that might float over to this thread, I'll share what he told me on this matter:

The first time you had received this, you had changed your Dropbox password, but it should be noted that these one time code emails can be sent when the incorrect password has been used when trying to enter the account. As such, if you have received such a message, even though you have changed your password recently, you may also want to consider changing your accounts associated email address.

This happens to prevent brute force guessing of user's passwords, but If there is anything else I can assist with in the meantime, please let me know.

...It's still worth noting to perform your security checks if you get an email such as the ones I did; you could still have a password breech on your hands. Be safe! But if you feel you are safe, then it is worth knowing that one-time code emails can indeed be sent about your Dropbox without any passwords being compromised, and can be just an indication of unsuccessful brute-force attempts of guessing your password. (I recommend changing your password just in case either way though!)

As the automated emails do not make this clear, I am so very glad Thomas did, and I hope this information helps someone else in the future. I'll mark this thread as resolved now. :)