An MPPT (Maximum Power Point Tracking) charger gives whatever is specified as its output, whether it's a 4.2V Li-Ion cell, or a battery of any other voltage, that should be specified on the charger. The maximum voltage and current at its output therefore are determined by the type of cell or battery it is made for.
You have misunderstood what the MPPT part refers to: it actually talks about its INPUT, which is the side connected to the solar panel.
Such charger monitors both the input and the output voltages and currents independently and will reduce the output current if the input voltage starts going down, but will not increase the output voltage or current above its set limits for the specific cell or battery, regardless of the input power available - if the battery is full, almost no current will be flowing on the output side, even if a noon Sun is shining and full power is available from the panel.
Likewise, even if the battery is empty and can take its full charging current, an MPPT charger will only increase its current until the input voltage starts going below solar panel's maximum power point.
A solar panel can only give a certain amount of current until its voltage drops too significantly, and this current depends on its physical size and the amount of light hitting its surface.
Most solar chargers on the market merely connect the panel directly to the battery being charged, and disconnect it once the battery is charged up.
However, the greater the voltage difference between the panel's output and battery's voltage, the greater will be the amount of solar panel's power wasted this way.
As an example, let's assume details in your case:
- Pmp (maximum power) = 10W
- Voc (open-circuit voltage) = 12V
- Vmp (voltage at maximum power) = 10V
- Isc (short-circuit current) = 1.1A
- Imp (maximum power current) = 1.0A
- Li-Ion cell voltage = ~4V (average)
If your charger merely connects the panel to the cell, the battery will draw all the current until the panel voltage drops to 4V, but since the panel can't give more than 1.1A, that will be the maximum current drawn, while the maximum power drawn from the panel will be less than half of its maximum power, or about 4.4W in this case (I will ignore charger inefficiencies).
If your charger keeps track of the MPPT, it will not allow the voltage at the panel output to drop below 10V AND will use its built-in DC-DC converter to drop the 10V to 4V while at the same time increasing the output current to 2.5A, which will result in the full 10W of the panel's power transferred to the cell, helping charge the cell much faster.
Or, if there is less light hitting the panel (due to Sun's movement or a cloudy sky), the panel will only be able to give out, for example, 2W or 0.2A, which, as explained above, would actually become about 0.8W or less than half of the available power without an MPPT circuit, which is often critical if your battery can barely get charged sufficiently during such times.
The "perturb and observe" is one of the methods used to track the maximum power point, where the solar panel voltage is slightly increased or decreased in steps (by decreasing or increasing the load on them) while measuring the output power. If such increase or decrease of voltage decreases output power, the direction of panel voltage change is reversed, but if the power keeps increasing, the direction of voltage change remains until the output power starts dropping.
These steps are done very fast so that they can keep track of the changing conditions (like clouds suddenly shading the panels).
Additional note regarding PWM: There are many cheap solar chargers marketed as PWM, and although some of them do employ PWM, it is merely a fast ON/OFF circuit without other elements like INDUCTORS/COILS which serve to transform the higher voltage and lower current into a lower voltage and higher current, basically giving nearly the same amount of power at the output as it takes at its input. If you open a "PWM" charger and don't see even a single (relatively large) coil/inductor, you shouldn't waste your time and energy with it.