As long as the 1/4" hose is less than 5 feet, it's fine to put the emitters directly in the main line.

Are you experiencing pressure drop along the different spaghetti hoses. Leaving the lines open at the end may loose to much system pressure to feed water along the entire mainline. Short mainline runs not problem but longer runs would make a difference in mainline pressure from beginning to end. Observe what is happening at the ends of the Spaghetti lines. Aloha

Thanks for your responses. These are all short runs of the 1/4" (spaghetti) lines. The longest is about 3 feet. Everything appears to be working fine. It just threw me for a loop seeing things reversed from what I am used to.

It's one of the ways to set up a low-flow system.

Here in the Arizona desert, all the professional installations are done "backwards" as yours. I believe it's a better installation (but I'm not a professional, just a bloke), because 1) it uses fewer parts, thus less cost and less plastic. 2) it also removes pressure on the spaghetti line, as the emitter is directly plugged into the main line. The "normal" way that most of the installation guides suggest, using a connector at the main line with emitter at the end can cause problems: I've had emitters crust over (our water is very hard) and I've even had emitters that popped off the spaghetti line. So even though it seems "backwards", it seems to be a better approach.