Maybe I'm misunderstanding you. "The voltage dumps" is not a technical term and I have no idea what you mean by it unless you mean that it drops from 30v to 16v when the BMS switches off, which is what normally happens.
1. You don't seem to be understanding what I'm saying. Your tester is measuring the voltage at it's connection to the battery. When the BMS is switched on, the voltage it sees is the cell-pack voltage. When the battery reaches LVC, the BMS switches off.
People would expect to see 0v on the connector at that point, but the mosfets that do the switching don't 100% block. Some charge still leaks through, but it's tiny.
The voltage you read with any sort of meter depends on the impedence of the meter. Typically, you see 12v to 18v with a normal DVM, but it could be anything between 0v and 30v. the voltage you see is absolutely meaningless. Effectively, it's zero volts because you can't draw any current from it. As soon as you try to take current, it collapses to zero.
2. In case you don't know, the battery's capacity depends on how much current you draw from it. The specification for the individual cells' capacity is normally based on a current draw of 0.2C, which would be 3A for a 15Ah battery. If you discharged at 16A, the capacity would be much less than the nominal 15Ah. How much less depends on the type and specification of the particular type of cells that are in the battery. I've seen as much as 20% less capacity when drawing 10 amps compared with the specified 2A. That's from a brand new and healthy battery.
In other words, your test results show a very healthy battery that's probably performing above its specification for capacity.
If you measure the voltage on the charge socket, you will probably get the true cell-pack voltage rather than measuring on the discharge terminals, as the charge mosfet doesn't normally shut off at 30v unless it's a crappy BMS that shares the mosfets between charge and discharge. Maybe your has shared mosfets, which accounts for the delay before you could charge again.