Question about tides

Maybe someone who is knowledgeable about tides can put me out of my
misery on a point regarding the simultaneity of neap and spring tides
all over the world.

In a book about tides, I read : "It is crucial ro realize that spring
and neap tides must each occur at about the same time all over the
world because the Earth rotates within the tidal bulges.

So far, so good, but  a few pages after that there's a passage about
tidal lags : "... there is a tidal lag, such that high tide commonly
arrives some hours after the passage of the Moon overhead. Because the
linear velocity of the surface of the Earth with respect to the Moon
decreases polewards, the tidal lag is greatest at low latitudes ...
but the precise lag is always constant for a particular location".

So after all, spring and neap tides can only occur at the same time of
day along the same line of latitude, where the tidal lag is equal all
around the Earth. At different latitudes, the tidal lag will make them
occur at different times. Am I right here?

James