You are correct that fusion takes place at high pressure in the core of the Sun, and not actually in the surrounding vacuum; gravity is what holds the plasma together. Strangely enough, the sun is a very inefficient fusion reactor, producing only 1 watt per cubic metre – luckily it is very big so the total is a lot of power. Here on earth we are aiming for efficiencies a million times better than that!
Plasma can exist at all manner of different temperatures and pressures – consider for example galactic nebulae, the aurora or fluorescent light bulbs, all of which are plasma. To achieve fusion within a plasma you need to have a combination of temperature, pressure (or density) and confinement – multiplying these parameters together gives a quantity that fusion scientists call the triple product.
It turns out that on earth, using magnetic fields instead of gravity, confinement of plasma is quite difficult. However we have been very successful at heating plasmas – we know how to easily achieve temperatures ten times hotter than the sun! So scientists have worked out the easiest and most efficient regime for us to aim for in our terrestrial fusion reactors, and that happens to be at quite a low pressure.
Part of this requirement for the vacuum concerns the relatively heavy atoms in the atmosphere (oxygen, nitrogen etc) which act as a major contaminant – interfering with the plasma to such a degree that it cannot sustain itself with even small amounts of these present. So, we can only form and sustain the plasma if we first make a very good vacuum before we inject the fuel.
Once the fuel is injected and heated the pressure in the middle of the plasma is about the same as the atmosphere.