When people talk about the Rays starters averaging fewer innings than other teams, they don't take into account the Opener effect.
If you use a two-inning Opener 15 times over the course of the year, your innings per start number is going to drop by about 0.3.
It's a little hard to see how often the Rays used an Opener last year, but they had 17 starts on three or fewer days rest, which points to an Opener. They had 20 games when a starter didn't pitch to any batters a second time. A starter could have been shelled, but more often that's an Opener.
So it looks like they used an Opener at least 15 times. It's not unusual an Opener goes less than two full innings, but even you use the 15 x 2 figure and add 0.3 to the Rays' 4.9 average, voila, they are above average at 5.2.
Eflin, Glassnow and McClanahan combined to average 5.6 innings per start.
The Rays don't "pull their starters early" -- they just use an Opener more often than other teams.