The roots of Trachelospermum are unlikely to damage house foundations, but planting a minimum of a foot away from a wall (whether its a house wall or garden wall or even a fence) is recommended practice for a couple of other reasons apart from air flow and possible foundation damage.
First, rain shadow - this refers to the fact that something planted right up against a fence or wall gets much less rain than something that isn't, and it may struggle to survive after planting. Second, any plant wants to grow all round, not just at the front, so planting a minimum of a foot away (preferably 18 inches, if possible) means the plant is able to grow all round, and is not obliged to produce growth only at the sides and front, which often then leans over and 'gropes' forward to get more light.
A foot away is the recommended distance even for clematis cultivars, even though the growth is not as vigorous and bushy as a Trachelospermum gets over time.
In respect of the other plants you say are planted too close to the wall, whether you can/should move them or not depends on which plant. If its a permanent shrub and has been in situ for longer than 3-5 years, then moving it successfully would be very difficult, so unless it has formed an unattractive growth habit because of being planted too close, or is a plant that will get very large indeed, best left alone unless there are apparent damp issues. If, though, it is a large or ultimately large shrub, then taking it out altogether might be wise; trying to move and relocate a mature shrub is often unsuccessful because of too much root loss when digging out. Large shrubs also have large roots and may interfere with foundations. Perennial plants can be moved, but are unlikely to cause structural damage to foundations anyway, so you'd only move those if they are leaning forward and not looking attractive, or if their presence is causing damp issues against the wall.
