When I look at a Battle Report (first screen snapshot below) I see little green arrows pointing upwards next to my ships.  I have assumed that those green arrows mean that my ships have gained enough experience to be upgraded.  However, when I exit the Battle Viewer and look at the ships in the fleet, the only ship that can  be upgraded is my survey ship.  This has been true for many of my fleets that have won battle after battle and none of the non-survey ships have gotten an upgrade.  The exception to this are my Command ships (ships with a Commander).  They earn upgrades as expected.

Please take a look at this.  I don't know if it makes a difference, but I am playing as a custom civilization.