Is this a case of a stale ISP DNS cache or did I fudge something up?

I am currently in the process of transferring a legacy website (from a legacy hosting service provider) to a modern solution. Due to my context-specific requirements (which include financial constraints), I made the decision to backup and replicate the website on a Digitalocean droplet (a virtualized linux instance) which has a static IP address 104.131.187.206. I have already configured everything appropriately, cleaned up the various loose ends that come from duplicating a Web application that is tightly coupled to its system, etc and the duplicate website is working perfectly fine.

Now, my goal is to point the existing domain name mcbc.on.ca to the new duplicate website on the DO droplet. The IP address of the legacy (shared) hosting provider is 216.251.32.98. Obviously mcbc.on.ca has been pointing to this address all this time. What I want is for mcbc.on.ca to point to 104.131.187.206. Furthermore, I am still using the legacy hosting provider for DNS and nameserver.

My task should be straightforward - simply modify the existing A entry for mcbc.on.ca in the Zone file so that it now points to 104.131.187.206. Now, I also wanted to keep an existing reference to the original website, so I added a new A entry for original.mcbc.on.ca that points to 216.251.32.98.

I successfully completed all of this yesterday and my DNS change has successfully propagated as of now (verified using this tool). FYI, it has been approximately 12 hours since I made the change.

My problem: For some strange reason, whenever I access the website at mcbc.on.ca, it sometimes resolves to the OLD address 216.251.32.98, and some other times correctly resolves to 104.131.187.206. I'd say the frequency is about 40% for the old address and 60% for the new address. This is obviously a problem.

Considering the fact that I've waited a good amount of time (although I understand that 12 hours is certainly less than 48 hours), as well as the fact that the tool I mentioned above shows that the DNS record has propagated to ALL over the world, my suspicion is that my home Internet ISP provider has a stale DNS cache.

My question: Am I right? If not, what do you think is my problem?

DNS doesn't, properly speaking, propagate. Records have a TTL (time to live), and that's how long other caching DNS servers should retain an existing lookup answer. You'll want to do some more self-education rather than go by thumbnail rules like "12 hours should do it."

If the authoritative nameserver is showing the correct results, that's the end of the story. Since at least some (as you say, most) other nameservers are showing the updated answer, you're done. You've done what you need to do, and in fact almost everything you can do.

(It's often a good idea to lower your TTL long in advance of an anticipated change, and you don't say if you did that, or what the TTL was to begin with. And since you didn't give actual details, we can't check.)

/Edit - now that we can see your TTL, it's set to 1 day. Presuming the TTL wasn't recently changed to that value, that means that anyone with the old record would have kept it for at least 24 hours after receiving that answer. The requestor (most often other DNS servers) would not re-query to see any change you made in the following 24 hours. In your case, at least 24 hours prior to the change, you should have dropped the TTL to the lower value your DNS provider allows.

If your home PC's upstream DNS provider doesn't respect TTLs, use a different one, and make sure your local cache has been cleared.