"Can't keep up" messages

Hello there. I just created a brand new server here. I basically came here because I was formerly running a self hosted server, but people couldn't log in. They used to get "connection timed out" errors every time they tried to connect to my server. So I created a server here, thinking that having the server hosted on a datacenter would help.
I tested with a friend and... it didn't work. Exact same error every time. We tried to figure out the problem, and came across the DNS flush solution. It worked fine. My friend can finally connect to the server, except the console is now sending me "Can't keep up! Did the system time change, or is the server overloaded?" messages on a regular basis, along with sometimes small lagspikes, whenever he joins.
What does it mean? Why does it do this? The server wasn't sending that kind of messages when I was the only one able to connect. My hypothesis is that my friend can connect when he flushes his DNS, but the server can't keep up with his low connection and then lags. Is that correct? Also the console gave me another message saying the server sucessfully set the idle timeout to 10 minutes. Isn't it something you're suppose to configure in the server config files? How can it change by itself?

I'm sorry for that block of text, and thank you in advance for your answers

Edit: I'm running a vanilla 1.12.2 version of the server with a randomly generated map.

So basically the server will send that message as long as there is a laggy player connected?

I'm sorry but I'm French so what does TPS mean? Also I do not use any Redstone or command block yet since the map is freshly generated, so it doesn't come from that. No plugins either.

Thanks for all your answers by the way.

Okay got it. Thanks!