Hi,
I think you are understanding the concepts perfectly, but misunderstanding the assumptions of Boyle's law.
In plain English, Boyle's law states: "The absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system."
Boyle's law assumes temperature and the amount of gas do not change. These are assumptions that reduce the number of variables in the system so we can isolate the relationship between pressure and volume.
On the other hand, Charles' law states that the volume of a given amount of gas held at constant pressure is directly proportional to the Kelvin temperature. Here we assume a constant pressure. Under these conditions for a fixed amount of gas at a fixed pressure if you decrease the volume the temperature will decrease, or if you decrease the temperature the volume will decrease.
However, in many situations, all of these variables (pressure, temperature, volume) may be changing at the same time. This is where the ideal gas law can be useful.
The equation is P * V = n * R * T, P=pressure, v=volume of gas, n=amount of gas (in moles), R=ideal gas constant, and T=temperature of the gas in Kelvin. * indicates multiplication.
So to get back to your original statement
"If the volume decreases when the pressure increases ... is that the temperature of the now pressurised gas decreases."
If we decrease volume, and increase pressure, we cannot be sure what happens to temperature without knowing how big those other changes are (and assuming the amount of gas does not change).
For example if we start with PV=nRT and we double Pressure and cut Volume in half we get 2P * (V/2) = nRT. This simplifies back to PV=nRT because we are multiplying and dividing the left side of the equation by 2, so no net change and no change in temperature. However, if Pressure increases by a factor of 4, and volume is cut in half then we are multiplying the left side of the equation by 2 (4/2=2), and thus must also multiply the right side of the equation by 2, and we get (4P)*(V/2)=nRT*2. So, if pressure goes up 4 fold, and volume is cut in half, then temperature (in Kelvin) is doubled because R is a constant and we are stating in the beginning that n (amount of gas) does not change.
Make sense?
Cheers,
Colin