In a token bucket algorithm you don't actually have a separate replenish step, it is baked into the next check you do. Similar to how in the example you linked the removal of the old entries is baked into the check step.

Check out my example: https://gist.github.com/ptarjan/e38f45f2dfe601419ca3af937fff... on line 23 with

    local filled_tokens = math.min(capacity, last_tokens+(delta*rate))

that adds in any tokens that should drip into the bucket since the last check.

There is no replenishing process, its just a conceptual thing. In code one just computes time difference and then multiplies that with fill rate to determine tokens to fill before deducting any. Token buckets are popular because they work well, require fixed size storage and are extremely simple to implement and test.