All funds transfers occur through the ACH network -- the same network that banks and employers use for direct deposit and that you might use to pay your utility bill. ACH is governed by Reg E, meaning that in the unlikely event of an erroneous or fraudulent transfer, you have 60 days from the date of your bank statement to dispute the transfer, at which point the bank must reverse the transfer and investigate. By contrast, wire transfers typically cannot be reversed.
ACH transfers typically take 2-3 business days to complete. Over the past few years, NACHA, the organization that oversees the ACH network, has been moving towards same-day ACH transfers. As a result, some transfers through Max now settle same-day or next day, while others can still take 2-3 business days.
As a result, a full optimization which involves the transfer of funds from savings to checking and then from checking to savings could take up to a week start to finish, but over time, this process should get faster as more banks move to the same-day standard. The entire process occurs automatically, but you can follow the progress by clicking on the word "Optimizations" atop your Max Dashboard.
If you ever need funds immediately, you always retain the option to contact any of the underlying banks directly and request a wire transfer. Marcus and American express will execute wire transfers for free, while the other banks impose a nominal charge for wire transfers, which typically amounts to less than a day's interest income for most Max members.