All of these people on here telling you to just evict the person. Great for them but they won't be paying the price for that decision, you will. You hired a property manager for a reason so let them keep doing their job. You hired them to collect the rent and you have said that they are doing that. I understand that you are frustrated that it is not all up front like you expected but they are getting it done and that is what matters to your pocket book. I have been managing properties for others and myself for more than 25 years. My guess is that most of the people here have only a few rentals. The more properties you have the more likely you will run into this. It is a numbers game and it sounds like you just got unlucky and got it early. This practice is not uncommon. The goal is to collect the rent and avoid eviction. Working with your tenant will get you a lot further than constantly fighting your tenant. Over the years I have had many tenants that have had to break their payments up into 2 or 3 payments, and they were tenants for 5-10+ years. It is not always a sign that things are going to go south. As long as they get paid by the end of the month they are fine. When it goes beyond the end of the month that is when it can start to become a problem.
What truly is your alternative? Yes you can evict them. What is that going to cost you? Depending on the state it could take you 1 to 2 months for the eviction and then potentially another month to get the property back. Now the tenant is out of the house you will have to fix it up so you are probably talking $1,000 - $5,000 for that, depending on how much needs to be done. You are also talking about another 1-2 months before a tenant moves in. Plus there is a leasing fee. So at a minimum you are probably looking at $3,000-$4,000 expense to you but that number could easily be up to $10,000 depending on your state's eviction proceedings and the condition of the property. To me this is not worth it to get rid of the annoyance of the pm company taking partial payments over the month. This is also why, unlike others, I said that they are doing their job. I think the better pm company saves me the $5-10k and does the extra work that they are doing in collecting the rent in payments and sending out all of the notices. Make no mistake, doing this is extra work for them. From what you said, while they keep late fees, they waive those late fees if the tenant pays the rent in full by the end of the month so they are not making anything on this.
I understand that it can be frustrating seeing this happen. This may sound bad but stop looking at the property financials mid month. Don't worry about it until after the month. There is no reason to be looking at the financials mid month.
As far as you being worried that the consistent late payments won't look good when you try to sell the property. It sounded like this is a single family rental or condo, but either way just a single unit. Are you planning on selling it any time soon? If you are, is this a specific market where there are a lot of places being sold to investors with tenants in them already? For single family homes the value is going to be based on the house itself. When you go to sell it I have found that most of the time it is best to sell it vacant. There are still a lot more home buyers out there than investors so if you are trying to sell it to just an investor you are going to limit your market and most investors are looking for a deal while many home buyers are just looking to get a home at a fair price and not have to compete against investors. If the property is a multi tenant property then that might have an impact, but even then I doubt it. Report ledgers are monthly and you don't see partial payments on them and most evaluations are looked at that way.