It should be automatic when you get the tech. The tooltip for the shrine may not change instantly, and the tooltip for mana income will not change until you press end turn.

It seems that the shard must be directly connected to the city for the greater shrines to take affect.  My first game is rich with shards.  The shards which connect to the city have greater shrines.  The shards which do not connect to the city have lesser shrines. 

I also noticed that the Temple of Essence can only be built if you have a shard connecting to the city (can't be built in cities with shards that do_not connect).  Mayhap there are other things which are "connection required"?

UPDATE: Somewhere between 5-10 turns after the shrine was incorporated into the city, it automatically updated to a greater shrine.  So it is confirmed that in order to get a greater shrine, one must connect the shard to a city.  If there was already a lesser shrine at time of the connection, the greater shrine update will occur automatically.  It takes time but eventually you will reap the greater benefits.

Just to clarify-- connect meaning within the ZOC?

I wish they would just change the shard mechanic to one of flagging ala HOMM or the old MOM spirits.  It would make hit and run tactics more viable against a stronger opponent.  Other improvable tiles (mines, clay pits stables, etc) could stil have to be within your ZOC. 

But magic shards... I would think your average villager would like to stay far away from such ominous remnants of past horrors.

If anything it will lower city spamming, I for one am too impatient to slowly expand my ZOC, I just build a settler... 

It's because it's such a subtle nuance it's practically a bug.

Right now, in the beta, it means your city must be close enough to the shard to actually touch it.

I found this quite irritating as well, especially if the shard is 5-6 tiles away, i takes forever to snake my city out to it.  Also, the shard has to be in the city for the +3 ess/turn improvement to be constructed.