The multiplier is an upper bound on money creation by banks, and it does not specify a timeline. That's a fact. Obviously, not every bank loans all the way to the minimum reserve ratio (for example, currently, the reserve ratio is zero in the US, which makes for a poor denominator). Nor does every recipient of proceeds from a loan put all of that money into a lending bank. However, the money supply is still increased via lending. The increase from the issuance of a loan is immediately reflected in total deposits.

What your link is stating is that central banks respond dynamically to the total number of bank deposits, and apply other policies (such as influencing interest rates) against that number directly, which can overpower the effect of the multiplier, if the central bank chooses. However, it does not nullify it, and it very much depends on a central bank taking that action. Your link also mentions regulations which may be specific to the UK about how banks lend, but the underlying principle of money creation remains unchanged.