FOUND_ROWS() returning incorrect value
Seems similar to this Bug #69166:  Wrong result of FOUND_ROWS() in MySQL 5.6:


  Description:
  
  Executing FOUND_ROWS() after SELECT SQL_CALC_FOUND_ROWS ... returns wrong result under certain conditions.
  Might be related to Bug #68458
  
  See steps to reproduce. ...


and of Bug #69119: Wrong FOUND_ROWS() on MySQL 5.6.11


  Description:  
  
  FOUND_ROWS() return is wrong count.


It seems they have not been fixed.

In any case, it would be a good idea to upgrade to latest 5.6 (5.6.33 currently). Both of your installations use very old versions. After upgrading check again and if the error persists, report it in the above bug item (69119).

Related to the upgrade: I don't think you have to restore for an upgrade in same major version. I's good idea to take a backup first, before the upgrade procedure, just in case something goes wrong.