You should NEVER flush tampons.
Tampon companies say they're flushable to seem more convenient - as long as they pass the Brunelle Flushability Test (toilet set-up in laboratory, tampon has to pass the U-bend - no consideration of low-flow or septic tanks, and no consideration of what happens to the tampons further-up the sewage system) they can call their tampons flushable and no one can tell them otherwise because they're self-regulated so the Brunelle test is their own standard.
Tampons are not flushable because they're wads of rayon or cotton that do not break-up in the water like toilet paper and they expand when they've absorbed fluid - basically they block pipes, in your case at least they won't block pipes further-up the system (this costs water authorities billions per year to fix and to send men down to unblock pipes), but it may still cause serious problems with the septic tank. For normal toilets flushing is also a problem as the tampons can get through sewage treatment plants and into our waterways, thus finding their way onto beaches - tampons are bad enough for the environment without this too.
ALWAYS dispose of tampons correctly - wrap them up, throw them in the bin.
WEN Sanpro - http://www.wen.org.uk/wp-content/uploads/sanpro.pdf
The Bag It & Bin It campaign - http://www.water.org.uk/home/resources-and-links/campaigns/bagandbin/about-bagitandbinit