Learn English – What does “pass it on” mean

"In time" and "out of time" can be a musical reference, referring to a time signature. Especially in pop music, "time" refers to the beat of the song.

For example if a musician says,

You are playing that rhythm out of time.

It means you are not playing the correct rhythms, maybe playing in the wrong time signature or adding / dropping a beat, or playing too fast or too slow.

When you are surprised, startled or scared by something, we say your heart "skips a beat".

When a heart beats in time, it is beating with an even rhythm.

So to answer your question, my interpretation is that he's making a poetic phrase which includes sentiments of being startled, but safe with the support of a loved one.

This is a standard idiom in English. The earth here is a metaphor that symbolizes the impossible, the immoderate, or the unfulfillable:

promise (someone) the earth (or moon)^NOAD
make extravagant promises to someone that are unlikely to be fulfilled:
interactive technology titillates, promises the earth, but delivers nothing

The origin of this idiom is probably from the third temptation of Jesus (in the Bible), where the devil tempts him with the ridiculous promise of all the kingdoms of the world:

Again, the devil taketh him up into an exceeding high mountain, and sheweth him all the kingdoms of the world, and the glory of them; And saith unto him, All these things will I give thee, if thou wilt fall down and worship me.
_{— Matthew 4:8–9 (The Bible, King James Version)}