There are no continuous "tenses". It is natural that you be confused because these misnamed "tenses" confuse every learner of English.
Consider the "Present Continuous" sentence:
"Billy is riding a bicycle."
"Riding" is not an active verb in this sentence. It has an object but no subject. The only verb is "is". "Riding" is a participle acting as an adjective. It is not an ordinary adjective (like "happy"), but a participle acting as an adjective. As such, it has some verbal characteristics (like having an object) without being an active verb (because it has no subject). "Riding" describes Billy, but Billy does not *act* through "riding" the way a subject would normally act through a verb. Rather, the linking verb "is" connects Billy with this adjective just "Billy" and "happy" are connected in the sentence
"Billy is happy."
One thing that might help to convince you that "riding" is an adjective (and not a verb) is that it *behaves* like one. An adjective clings to the nearest noun, and a participle does the same. Consider these sentences:
1) Riding a bicycle, Billy saw a cat.
2) Billy, riding a bicycle, saw a cat.
3) Billy saw a cat riding a bicycle.
In #1 and #2, the adjective phrase ("riding a bicycle") describes Billy because Billy is the nearest noun. However, in #3 it is the cat who rides the bicycle because "cat" is the nearest noun.
To help yourself learn to use participles correctly, write more sentences in the style of these three examples, and fewer sentences in the form
"Billy is riding a bicycle" (Present Continuous)
Once you have a better understanding of what participles really are, you can resume your use of the Present Continuous Word Pattern, and this "tense" will no longer confuse you.