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The official Scrabble rules contain the following:

Premium squares only count on the first turn they are used on. If a subsequent turn uses a letter that was previously placed on a premium square, the tile on that square is only worth its face value.

The only time a premium square is active for more than one word is if more than one word is created with a letter on a premium square on a single turn. Only use premium squares that are under tiles used in a given word when calculating point totals for each word created in a turn.

For example, if you create ‘jobs’ and ‘cakes’ by adding the ‘S’ tile to the end of the existing word ‘job’, and the ‘K’ tile is on a red square, you would count ‘jobs’ for its face value (13) but you would triple the value of ‘cakes’ (30) and your total for the turn would be 43 points.

I find this a bit confusing. Can it be explained further?

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    Can you add a bit about which part of the explanation isn't clear to you? That way we can take away your doubts instead of just paraphrasing the exact same rule. – Erik May 8 '19 at 9:24
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The premium square's bonus only counts on the turn in which a tile is placed on that square.

It doesn't count on subsequent turns, even if a new word using the tile on that square is made -- only the base points for that tile are used in scoring the new word.

So each premium tile's bonus can only be used once per game. (EDIT: once as in "one turn", not "one word". If you place a tile in that space that is part of two new words in one turn, you get the effect on both words that turn.)

The easy way to remember this is that: once you can't see it (when considering your play), you can't use it.

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