I was suspicious about this quote as I thought tissue paper wasn't invented [1] when Rutherford said that but apparently Rutherford said this retrospectively in 1936; not in 1909.
Among the applications of tissue paper listed at your link, are toilet tissue, facial tissue, and paper towels.
It also mentions "household towels" which doesn't make sense to me, surely they don't mean what I am used to.
In my area of the US, however, "tissue paper" out of context doesn't imply any of those, I don't think, rather it's the stuff used to wrap gifts or maybe to crumple up to pad them in a box. The stuff is also crumpled and put in new shoes, for instance.
It doesn't strike me as that odd to call toilet paper and facial tissues "tissue paper" although I don't think it's common; however calling paper towels or other towels "tissue paper" seems strange.
[1] Kleenex introduced the facial tissue in 1924