I myself have a personal Microsoft account based on my work email address...that I've had for many many years (pre-365 years)...and then when 365 came out we jumped on that...of course..work email address for that too. It's really not a big deal. Things still work great.
Couple of ways to work this.
*...ANY time you log into office.com you should be presented with a CHOICE of "Log into your work/school, or log into Microsoft <personal>". You click the work/school. Once the apps are set the first time...they should remain settled.
*If the computer was setup with the user profile as the personal Microsoft account, nuke it, join AzureAD...and then log in with the Azure profile which will set that user profile as the work/school account and lock it in from there. Just like if you had a local active directory, any...rather...ALL...workstations you setup on that network, you have them "join the domain"...right? You don't leave workstations in "workgroup mode" for those. So with 365..set them up right...join AzureAD. It lets everything drive home perfectly...and all the computer profiles (MEMs version of group policy) you setup for the computers properly take hold and everything runs like a dream.
I have quite a few clients that have both personal and work MS accounts with the same password. Not my job to manage their personal MS accounts, but I never let them interfere with their wok accounts. Microsofts login will always challenge you with that "choose a work/school account, or your personal account" popup...where you click on the one you want.
So..join AzureAD.