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The charger must allow you to adjust the CV (Constant Voltage) setting.
If the factory needs to set it for you, then tell them to set it at a voltage of
N * Vcell-max
where N is the number of cells in series, and Vcell-max is the maximum cell voltage:

• 3.6 V for LiFePO4 cells
• 3.8 V for LiFeYPO4 cells (Thundersky-type: Winston, Sinopoly)
• 4.2 V for LiPo cells and standard cobalt cells

If the charger has a control input to enable it, the Lithiumate can use it to control the charger, instead of controlling the charger by switching its AC input power on and off. This allows the use of larger chargers, whose AC input current exceeds 16 A. Also, you may decide that it takes less effort to wire the BMS master to the control input than to splice the AC power cord at the BMS master, on its way to powering the charger.

While an enable input will let you use a larger charger, the limitation remains that the output current must be within 30 A, so that may not buy you much.

Here is a list of available chargers.