the beds will have spuds in them..
Because you mention this I think I would use it at planting time rather than create two lots of digging.e.g
Dig you potato tench/s a little deeper than you would have, had your manure been dug in earlier, then add a layer of manure in the bottom of the trench and plant your potato seed on this, back filling as you go on.
Now there are those who will say this takes out all the nitrogen from your soil and they are not wrong but only at the lower levels in the soil.
What you have to remember is; the growing process of the potato, and indeed the tomato and that is;
the moisture seeking roots are on the bottom which in this case would go into the moisture retentative manure, the feeding roots which ultimately produce the potatoes will grow horizontally into the soil above the manure.
Plus if you earth your earth your potatoes up you deepen this soil level thus encourage a bigger root system resulting in 'more potatoes'
As Saddad mentioned; some peoples ideas will differ and as you see 'my view' differs!
And as I mentioned before; my way reduces the digging aspect and anything that reduces that is good in my book!!