Not too sure if this question should be here or not, but regardless.
Should a leaflet have 'turn over' written at the bottom centre to let the viewer know there is another side, or will they automatically/instinctively look at the other side?
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'Should' is pretty black and white and we don't work in those terms.
Is it helpful to the user? Yes and if you have the space, why not be more helpful to the user?
As noted by @HarrisonPaine in his comment on the question, "See Reverse" or "See Other Side" is more common verbiage, but yes such a note is always useful, especially if there is enough information on the front side that the user might not inherently consider to look to the other side for more. If you have the space you might want to add "for more", "for more information", "for more details", etc.
The addition of the circular arrow in your example is definitely helpful too. In an online context that might be mistaken for "refresh" or the like, but in printed material obviously it's not "refreshable" so for folks that might not immediately understand what the text means (especially if your target audience may not be fluent in English and your leaflet is multilingual or has diagrams/images intended for them) they can still get the idea that they should flip the leaflet for more.
If it matches stylistically, you may consider a "3D" flip arrow instead, such as the "√" character in the Wingdings typeface:
Need more info
Is the design pattern you have intuitive to the user? In other words, will a person know that a leaflet is interactive and can turn over?
In the UK, the traditional term for this is to put P.T.O. at the bottom of the page (Please Turn Over).
It doesn't hurt to include it as a physical leaflet may ( or may not ) have two sides of information .