Yes, your interpretation and ruling was spot on. Not only is Blink a VERY useful defensive tool for mages (you know how squishy they can be sometimes) as it COMPLETELY removes them from harm and detection save for things that can see into and effect the Ethereal Plane, Anything that might do Force Damage where the caster is standing, as well as anything that might happen to the caster during his or her brief stay on the Prime Material in between blinking; but it also does NOT require concentration, allowing that same spell caster to use its concentration for other nasty things in between blinking out of existence.

Most of my players do not believe that the spell would allow a character, should they roll 11 or higher at the end of their turn, to avoid attacks, spells, and other hazards when their character is not acting.

But that is PRECISELY what this spell is meant for and supposed to do. That's why it costs a resource (Spell Slot) to cast, and requires a good roll to actually work and remove the caster from combat until they appear again next turn.

If they need a realistic description of the spell? A ROUND (everything taking 1 turn in the initiative) happens in the span of 6 seconds. So every 6 seconds our dear mage who cast Blink is appearing for a brief moment to do something, then vanishing again to the Ethereal Plane. Every 6 seconds; thus appearing to be blinking in and out of existence upon the battlefield and giving us the namesake of the Spell itself.

A few counters to this spell include:

• Counterspell it as it is being cast (Perhaps one of the obvious ones)
• Dispel magic
• Etherealness
• Any area protected by Forbiddance
• Forcecage
• Magic Circle
• Mordenkainen's Faithful Hound (Can see into the Ethereal Plane)

And that was just half of the spell list I browsed. This doesn't even touch on potential creature abilities that could nullify the effectiveness of Blink, or a creature waiting in the Prime Material plane for the mage to blink back into existence for the duration of it's turn and ready an action just for that very instance. So it is certainly not a fool proof guarantee of safety, even when the dice are in Blink's favor.

While it's not spelled out explicitly that you take no damage, the intention seems to be that you take no damage.

You fall 30ft per round, which is about 5ft per second, which is much too slow to be taking falling damage. (Even slower than Feather Fall, which is 60ft/round)

Keep in mind that you're descending at a regular walking pace, and you are free to land on your feet at the end.

Do keep in mind that the "slow fall" feature only works while you are using the flying option of the boots. If you just drop off a cliff without flying, the boots will not protect you.