Na and K are incompatible in the mantle. Low degree melting that occurs deep in the mantle forms magmas enriched in Na and K. Magmas formed due to hot spots are formed deep in the mantle.
Tholeiitic basalts are voluminous magmas that form due to decompression of mantle rocks. The mantle then melts to a rather large degree at low pressures to form a relatively reduced magma (therefore tholeiite and not calc-alkaline). Their relative depletion in incompatible elements stems from the fact that the mantle peridotite being melted is a recycled rock, which lost it's incompatible elements long ago.
On the other hand, alkali basalts are produced in smaller volumes than MORB (mid ocean ridge) tholeiitic basalts. OIB (ocean island basalts) are commonly alkaline, but alkaline rocks are not restricted to oceanic settings. They commonly occur on top of hot spots and rift zones, regardless of the nature of the lithospheric plate which they erupt though (oceanic vs continental).
I.e. Is it that the ions (Na and K) are more incompatible than the Calcium ions found in the tholeiites? Why is this?
Yes. Sodium and potassium are less compatible than calcium in minerals that comprise mantle rocks. This figure, taken from my answer to What are the high field strength and large ion lithophile (HFS or HFSE & LIL or LILE) elements?, shows why:
MRFE stands for Mantle Rock Forming Elements. These elements are compatible in olivine, pyroxene, garnet, spinel and anorthite. Na and K are only monovalent and larger than the MRFE. Thus, they are compatible and in cases of mantle melting, they are partitioned to the liquid (i.e. magma) phase.
In order to understand why this enrichment in Na and K occurs, we need to understand where in the mantle these magmas form. Whereas tholeiitic magmas form in shallow depths, alkaline magmas form much deeper. Experiments show that the silica undersaturated nature of these rocks requires very deep melting (tens of kilometers). Since the melting does not occur by decompression, it has to melt by heating: a hot spot. This hot spot melts mantle rocks that did not experience prior melting events by the "ocean conveyor belt", and thus still retain their incompatible elements, including Na and K.
There are two other possible sources of Na and K enrichment in alkali rocks.
- Mantle metasomatism: Na and especially K are LILs: They are highly mobile in fluids. It is possible that mantle rocks were metasomatised by K and Na bearing fluids. This would cause minerals such phlogopite (a mica) and certain varieties of amphiboles to form in the mantle. These minerals are readily melted, thus contributing Na and K to the alkali magma.
- Contamination by crustal rocks: This process is especially important in continental rifts. Continental crust is rich in Na and K (micas, feldspars, amphiboles) and these elements can be easily assimilated to the rising alkali magma.
why it is that alkali basalts are more 'mature' than tholeiites?
I'm not exactly sure what do you mean by 'mature' but I will address the timing of alkali magmatic activity. Here is a very simplified depiction of what happens:
At first (A), a young plume will still be deep. The melts that it forms are low degree and deep. Then, when the plume 'matures' (B), it causes shallow melting producing voluminous tholeiitic basalts. The margins of the plumes still produce low degrees alkali melts. When the plume wanes (or just migrates somewhere else), you get only alkali melts again (sorry, I was too lazy to draw C in the figure, but it should look not too different than A). This is similar to what's happening at the moment in Hawaii. The newest (still underwater) volcano, Loihi, erupts alkali magmas. This corresponds to stage A in the figure. This is also what the oldest rock on Hawaii (the island) are made of: alkali rocks. Most of the rocks by volume on Hawaii (again, the island) are tholeiitic basalts erupted some hundred thousands year ago, corresponding to stage B in the figure. Recent (geologically) eruptions are yet again alkaline, similar to stage C.
For some extra reading about alkali rocks and related subjects, see these other questions and answers: