Probably. But that’s a CSP issue, as I already said. Somehow, the server did not deliver the stylesheet with the correct MIME type. This could be related to SSL, in which case getting your own certificate would probably not make a difference.
I don’t know enough about Safari but I could imagine that it gets kind of picky when SSL is active so that it refuses to download the CSS (or other resources) if they look fishy to it (again, the relevant term is CSP in this context).
The network view you posted is less helpful then the console tab in this context. I’m not even sure that the network tab would show errors.
What exactly is it that ngrok is supposed to be doing?
Just to make the terminology clear: you can’t buy SSL, you buy a certificate. And you do that for a domain (dtserv.ngrok.io, for example), not for an address. I know that this may sound overly picky, but it helps to use the right terms when trying to solve a problem.
And no, you should not have to buy a certificate for this domain. At least if the browser is not too restrictive, it should offer you the possibility to accept the certificate although it does not match the domain name.
Also, there already seems a certificate issued for this domain as shown in the page information. You could check that by inspecting the certificate information by clicking on the lock in the address bar.
When I try your server dtserv.eu.ngrok.io, I get
Tunnel dtserver.eu.ngrok.io not found
ERR_NGROK_3200
If I understand you correctly, you’d basically need a DynDNS service. Ngrok seems to do a lot more than that (secure tunnel - whatever that might mean and why would one need it with HTTPS anyway?). Maybe another, simpler DynDNS service would solve the problem.
Also, DEVONntech might check the CSP in their product. At least Firefox is not happy with it. But it should be: a broken CSP sooner or later leads to a broken app, in my experience.