If the titan transformation is immediate once a titan eats a shifter, how did Santa Titan not become a shifter when he ate Eren? As we see from the Manga 


  when Eren ate his dad and when Armin ate Bertolt, they immediately transformed into a shifter-titan. 


But when Eren gets eaten in Season 1, how is it that the titan who ate him never transformed. Plus Eren was inside his stomach for a while before he transformed and killed him.
The proper requirement to gain the powers of a shifting Titan is to drink the spinal fluid of the Shifter. This is revealed on chapter 65. The "Santa" Titan didn't gain any powers because he ate Eren whole. 


   When Eren ate his father, he bit him on the waist, severing the spine and getting access to the fluid. Armin bit Bertholdt on the head.