How are you connecting? Internally or externally (are you getting your ip from the ipconfig command in the command prompt or from a website). If you're not, try connecting internally. Also, I'd really learn how to port forward (there are thousands of tutorials for Minecraft port forwarding everywhere) as Hamachi lets viruses in everywhere and can really mess up an internet connection. Also, keep your firewall on!
It takes longer because the packets are travelling a longer distance
If you're using the domain name, it doesn't know where that is. So it asks, and gets an answer: your public IP address.
It then looks up how to contact that IP address. It doesn't know that IP address goes to itself. So it asks your router, which also doesn't know, which then asks your Internet Service Provider's routers, which may know, or may pass the request further out, until it finds a server that knows how to contact that public IP address.
Finally, it reaches a server that can see that public IP address and then it creates a connection between your computer and that computer — which is your computer but it still doesn't know that — and passes messages back and forth along that whole chain. So when you use your public IP address, your Minecraft client and server are talking to each other over a long loop that goes way out into the public Internet and then back through your ISP to your computer.
That's a lot of extra time for your Minecraft client to finally get to talk to your Minecraft server about each tick! By comparison, using your actual IP address makes only 1 hop (or, if your network is configured cleverly, none), which is much faster.
To draw an analogy, connecting to your public IP address via domain name is like sending your roommate a note that it's their turn to clean the kitchen by putting it in an envelope with their name and address and sending it through the national mail system, when it would be much faster to just slide it under their bedroom door.
To illustrate this with numbers, I sent a set of tiny messages (pings) to my public IP address. The average ping time for that long round trip was 2.335ms. Sending the same thing to my actual IP address was 0.105ms — a 22× speed improvement. It was slightly faster even when I used the shortcut IP address that means “this computer” (127.0.0.1, also available as the DNS name localhost), at only 0.094ms — a 25× speed improvement.
So the moral of the story is, when connecting to a Minecraft server on the same machine as your Minecraft client, always use the domain name localhost instead of your public domain name or IP address.
Best Answer
I'm going to make an educated guess and say you told them the new address mere minutes after creating the A record, right? That's the source of the problem.
DNS changes take time to propagate across the Internet due to caching and Time To Live rules. If you told them to connect right after you created the A record, it would not yet exist in their ISP's DNS servers.
For reference, I can ping your new subdomain successfully and I can connect to it using Minecraft (though it immediately kicks me out because it's whitelisted), so your friends should be able to connect now or soon, unless they use an ISP that is particularly slow to update their records.