You don't need to upgrade or compile anything.
The document you reference state that you should update from 1.0.1 to 1.0.1q because of CVE-2015-3194, CVE-2015-3195 and CVE-2105-3196. However, if you run:
rpm -q --changelog openssl | grep CVE-2015-319
you should get:
- fix CVE-2015-3194 - certificate verify crash with missing PSS parameter
- fix CVE-2015-3195 - X509_ATTRIBUTE memory leak
- fix CVE-2015-3196 - race condition when handling PSK identity hint
which means that these fixed have been retrospectively applied to your version of openSSL.
Distros don't update their versions on every time upstream release, as these releases are relatively new and untested. Instead they cherry-pick the patches that they will apply. Usually, this means security patches or regression fixes only.