How important is soffit ventilation with tiled roofs?
Attic Ventilation shall be “cross ventilation “ and shall be 1/150th the area that is to be vented. (See ICC R806 Vents.) 

However, there is one exception: The attic ventilation can be reduced to 1/300th the area to be vented provided one of the following items are met: 

1) a Class I or II vapor retarder is installed on the “warm-in-winter” side of the ceiling, or 

2) not less than 40% and not more than 50% of the ventilation is located in the upper portion of the attic. The upper portion is defined as: “Upper ventilation shall not be lower than 3’ below the ridge or highest point of the roof. “  (See ICC R806.1.2.)

Also, the Code says you’ll maintain a 1” clearance between attic insulation and framing. 

So, you can see there is clearly a benefit to having ridge vents, gable vents, etc. , but in a proportion that allows COMPLETE CROSS-VENTILATION to the attic....and cross ventilation is best with soffit vents. 

Remember, you’re venting the attic to remove condensation. Condensation damages wood, not your tile roofing. I’d act quickly.