In Anima, fumble can only occurs on a **natural** 01-03 (01-05 with disadvantage).

The rules about fumbles are quite easy (as described in Core Exxet - p.007-008): 
> When the player rolls a **natural** 01-03 the action is automatically failure. You then  have to proceed to the level of failure by rolling a non-opened D100. 

For an opposition roll (offense action vs defense action, search vs hide, etc) you substract the level of failure to your skill. In the case of initiative, you substract a specific value (Core Exxet - p096-097).