Eccentric bottom bracket is neat idea for adjusting chain tension on singlespeed/gearhub bike. Basically, you can have vertical drop outs on the frame and removing installing rear wheel is always the same you don’t have to worry about adjusting chain tension like with horizontal drop outs. (and tensioners looks ugly IMHO)
For adjusting mine (Charge grater) I use 4mm Allen key with torque wrench plus pin spanner. I’m not sure about make of this particular EBB shell but is pretty much same procedure (sometimes tightening method is slightly different). Instead pin spanner circlip pliers can be used, and obviously when torque wrench isn’t available normal Allen key can be used with care (pay attention to not strip alloy thread)
First undo the 4mm Allen bolt all the way until BB body is moving freely inside its shell.
Next using pin spanner rotate whole body until chain is tensioned properly.
“Properly” is relative. I’m considering as adjusted, when I can move chain up and down around 2cm. Note that when the bolt is tightened back, the chain tension will increase.
If it’s to tight after tightening bolt to required torque, make mark on the shell/ebb body with pen, unscrew the bolt and turn whole insert just a hair using pin spanner. Tighten it back again. Recheck chain tension again.
Adjust saddle if you feeling the position has been noticeably changed relative to bottom bracket.
This is only the procedure to adjust chain tension, but once a blue moon you need to remove whole ebb shell, bottom bracket, clean everything thoroughly, re-grease and assemble back again (all this is relatively simple comparing to final step which is adjusting ebb)