Catching additional animals with a full pasture isn't an issue normally as the game will give you a prompt asking which animal you want to release in order to accept the new catch.
Those mammets though, they seem to have other ideas.
If all of your animals are under care, give up catching any rares. It will run away before you get a chance to end the caretaker and go over to catch it.
I make it a point to tend to the pasture and crops before anything else precisely for this sort of thing.
I also wouldn't use the automated care option either. It's 200 cowries a day and saves you basically 60s.
It saves 60 seconds per day (plus travel time) but you only need to collect every ten days at minimum, or every twenty days for crops.
Collecting animal leavings is only worth the money if you're crafting with them, though.
It's not that it's "real time rather than Eorzean" but that regardless of how the weather is tracked, you need to wait for the right combination of day/night cycle and weather, which can happen at inconvenient real-world times.
The game weather is primarily tied to the Eorzean clock, with weather changes at 8am, 4pm and midnight ET.
Joke's on you, I only have roughly 60s a day to play XIV so it works out perfectly~!
Besides, when you are raking in 600+ crowns a day, paying for NPCs to automate a facebook game is a pittance. I COULD have gotten my bike earlier but this game already coerces me enough to log in daily so it works out in my case, lol.
Fair enough if your time is that restricted. But it's not difficult to click on each animal/pasture once a day.
It's 1400 a week, 2800 if you throw in crops as well.
2800 thrown away to automate HALF of a process. You still need to click on each animal in the menu.