So the real problem is that Safari is slow, not that you are getting an application memory error message?
Although you still haven't identified exactly which version Mac Mini you are using, it is highly likely that your system has multiple "cores" in the CPU chip. What Activity Monitor reports is the percent usage of ONE such core, so, for example, if you have 4 cores, 100% means 100% of one of the four, leaving the other three idle. Right now, as I enter this, AM reports that Safari on my system is using about 1.3% of one core. However, if I got to a website with Flash video and run the video, that usage will skyrocket to something much higher, so high that the fans on the MBP begin to run harder. But I don't get any messages about "application memory" being in short supply.
What does AM show for memory usage? To see, click on the Memory tab and then the Memory column header to get it sorted with the biggest users at the top. Also, under Mavericks, at the bottom of that window is another set of information, including Swap Used and Memory Pressure. What do those show?
Safari normally runs pretty quickly, but if you have ISP issues, you'll see slowdowns in response times to some websites. Extensions to Safari can also slow it down, as do various third-party task bars.
So, again, is the problem slow Safari or application memory?