Spoofing this eye is significantly easier than spoofing a fingerprint, because modern fingerprint technology detect if a fingerprint is "alive" by looking at sweat pores, pulse, veins under the skin and other features of a living finger.

CCC reported that they managed to bypass Apple's Touch ID in 2013, so it doesn't really seem like one is easier than the other.

AppleID from 2013 may not have included all the features of AppleID in 2017.

But do phones check for all those markers?

Well, maybe. Usually flagship phones gets the best (most expensive) chips. Budget phones gets knock-offs.

It depends on which fingerprint hw/sw the phone is using. There are about 4 large players in the phone fingerprint chip space that have 90 percent of the market. Fingerprinting is heavily patented so all four vendors have their pros and cons. A few dozen small players competing about 10 percent of the market. They probably don't do much of it.

Do you know where I could read more about the ways fingerprint scanner detect that it's a human finger?

Sounds pretty fascinating.

Just do an internet search for "fingerprint liveness detection". Google Scholar has enough reading for a night or two.