What is most likely is that the junction of window to cladding is leaking at the jamb and sill.
Sill flashings were not a requirement for direct fixed fibre cement claddings until 2004. Prior to that James Hardies literature said something like - sill flashings give good long term protection - but were not a requirement. The joinery flange at the sill simply overlaps the cladding sheet by 10mm and is supposed to be open to allow any moisture entering above to drain to the outside of the sheet below. These are often closed off with sealant or plaster by both professionals and home owners not realising they are inhibiting drainage.
The jambs are supposed to have either a bead of sealant between the joinery flange and cladding sheet or a closed cell foam strip. The problem with sealant is that the thermal expansion of the aluminium joinery is far higher and if not installed as a proper sealant joint (bonded to surfaces only on 2 sides) can tear on stretching leaving gaps that allow water entry. The problem with closed cell foam strips is that if they are compressed too much the cells rupture and stay closed instead of pushing outwards to maintain the seal between the two surfaces and again the resulting gaps allow water entry.
An even bigger problem is when sealant or foam strips are not installed at all then prevention of moisture is reliant on either paint and/or the texture coating adhering to the joinery which again can not match the higher thermal expansion of the aluminium and therefore fails and leaks.
It is possible that you have issues around all your exterior joinery and I suspect along with others here that a full re-clad may be necessary to repair properly and legally. If that ends up being the case don't rush to install the same cladding again but on a cavity - take your time as there are plenty of cladding options with similar installation costs that can add significant capital value thereby partially mitigating the repair cost - and of course make your house look far smarter.