There are a few other methods that could deposit funds on the same day, but I wouldn't sweat it.

They just texted me and no other means of communication.

Every lender will have their own method/calculation, but most lenders will assume some amount of a minimum payment and apply that in your DTI calculation. 

I am considering as a first time buyer to utilize the BRRRR method on my personal home, while also using a 203K loan to finance and rehab the property.

I followed a BRRRR method. 

It's the same method used for security deposits.Congratulations!

I am also trying to find a partner to do the BRRR method but I need to ensure the person I am working with is trusted.

I like this method, but I've noticed more banks are charging hefty fees for these types of transactions.

With regard to giving a tenant leeway, its very short sighted to evict a tenant with a VERY strong track record for a VERY small shortfall one month, especially when they have been communicative and given you what sounds like a reasonable explanation as to what is going on.

The key here is open, contractual communication.