Is what I did correct, in attempting to resist the waswas (whispers of the devil) by intentionally swallowing my saliva? And did my fast become invalid, necessitating expiation, after I doubted tasting perfume from a tissue and swallowed saliva that was mixed with this doubt?

It appears you have a significant degree of waswas (obsessive whispering/doubts). The most important cure for such waswas is to disregard them and turn away from them. The fundamental principle for all acts of worship is validity. Your doubt about the validity of your fast does not invalidate it. So, do not invalidate your fast by expelling saliva or wiping it with a tissue. Your fast is not invalidated by swallowing normal saliva in the mouth or tasting the wetness of the lips. We do not believe that deliberately swallowing saliva when you feel a strange taste, as a way of defying the waswas, is an effective method to repel it. Rather, the effective method is to disregard such waswas, turn away from them, and seek refuge with Allah Almighty from the accursed Satan. As for your second question, your fast is not invalidated by swallowing what you tasted, and there is no qada' (making up) or kaffara (expiation) upon you.