Did you aleady read page 11 and 12 of this document, chapter 5.1, about Prevalence of Vulnerable Systems and 5.2: Countermeasures?
If your system is really vulnerable, then yes, you have to flush cache of sensible information before accessing suspect web pages.
But if your cryptographic tool uses non-cached memory, they are not vulnerable...
You could use NON Intel or single core CPU... or ensure no Sandy Bridge, nor Ivy Bridge and no Broadwell micro-architectures are used in your hardware.
Second time reflection
For my understanding, this paper is more a proof of concept than a exploit cookbook.
Cache attack is possible.
Regardless of requirement for this demonstration.
In fact, new multi-cores processors are insufficiently protected, due
to performance challenges.
And new optimisation at libraries level could make some unattended backdoor.
This exploit is hard to reproduce, but show that if processors constructors don't care, futur could become hazardous.