This is due to DNS propagation only. During this time what is happening is that the DNS servers which your computer is configured to use (possibly set by your broadband router using DHCP, and likely pre-configured or assigned into your router by your Internet Service Provider), are not yet reflecting the changes you have made -- but the DNS servers that the Anonymouse service uses are using the updated records.
While you are waiting for your site to be accessible from everywhere with the right IP addresses you can check using this free propagation check website I use my self regularly for the same purpose (don't worry if not all return a result since some apply rate limits to the number of requests from this service per day, but it does often help reveal when some are not resolving to the correct IP addresses:
This service checks a variety of DNS servers from around the world but obviously does not check all DNS servers - it can only give an indication of when it is likely that propogation may be mostly complete.
It is always worth checking both A records since they are independent and may take different lengths of time each to propogate.
According to IntoDNS (which I would recommend from experience) your DNS server setup and configuation is healthy.
The TTL (Time-to-Live) for your A records: 86400 seconds = 1440 minutes = 24 hours.
Therefore the maximum time you should have to wait for propogation to complete for changing your A records is 24 hours (can't always be guaranteed).