But your writing system overflowed before your finger overflow. That's not very intuitive. Each finger represents a unique glyph until suddenly on the last finger it takes two glyphs to represent it.
If you were using base eleven you'd put your pebble down when you hit dec(11) aka base11(10). That pebble represents dec(11). Then first finger would be dec(12) aka base11(11) and once again your first finger represents 1.
So in base11 [1,2,3,4,5,6,7,8,9,A] - pebble - [11,12,13,14,15,16,17,18,19,1A]
A pebble and five fingers would be dec(16) instead of dec(15) but your five fingers still represent 5. The pebble represents 11 instead of 10.
But really, once you're into double digits you normally wouldn't be counting on your fingers anymore. You write 10.