Could you please elaborate more on the issue that you’re currently experiencing? If the host/droplet is online ISPs should be able to access/ping it without issues (when using the IP address) if they’re not blocked of course.
If there is a DNS propagation for the domain name and you’re trying to access it using the domain name and not the IP address this can explain why some ISPs are having issues to access it. DNS changes might take up to 72 hours or even more due to ISP cache and normal DNS propagation. However this usually happens a lot faster.
When it comes to DNS propagation there is not much you can do except of setting a lower TTL for the DNS records (A records) in order to speed up the process a bit. As mentioned usually the DNS changes take longer time due to DNS cache from all the IPSs.