What does it mean for a game to be 'Caylus-like'?
The four distinguishing features of Caylus are


It's a worker placement game.
It has perfect information - you know everything about the state of the game, and nothing is hidden.
It has a clever and unusual turn-order mechanic, which is complex to play well, and absolutely critical to the strategy.
It has no luck. Like chess, there are no sources of randomness in Caylus.


Someone describing a game as Caylus-like can be referring to any of these fairly unusual characteristics. In your example, the Family version of Agricola is "Caylus-like" partly because it is worker placement, but also because there are no Minor Improvements or Occupations, so no cards held in hand, so there is no hidden information.

I play this game fairly regularly, and I have to say, it's pretty special. Other games often share one or more of these features, but the combination of mechanics is unique to Caylus.