Time to head for the high grounds

Your family's phrase ('familiolect' in linguistic jargon) is not so much misquoted or garbled as it is a lengthy variant of a common phrase that embeds the English lexical item, 'high ground'.

The first evidence of 'high ground' may be in the 1484 translation of Christine de Pisan's Here begynneth the table of the rubryshys of the boke of the fayt of armes and of chyualrye whiche sayd boke is departyd in to foure partyes: "Fyrst he shall see that the place be of a hyghe grounde…". OED shows "1489" as the first printing of the de Pisan translation, and finds evidence of figurative use of 'high ground', in the sense "esp. a position of advantage or superiority in a debate, moral issue, question of policy, etc." as early as 1800.

The phrase 'high ground' is often found embedded in the longer 'head for high ground', which means, generally, "go to a place of safety". Imperative elaboration of 'high ground' in this form is especially common where floods, tsunamis and lahars are likely to make low ground dangerous or untenable.

Use of the plural 'grounds', uncommon outside of your familiolect, may represent (at least for the speaker) a jovial mollifier of what otherwise might be an unalloyed imperative phrase.