Yes, Pentecostalism is inextricably linked the eschatology, because eschatology is one of the primary tenants of Pentacostalism, and it would be hard to say you were a Pentacostal, without also subscribing to eschatology. Eschatology is the belief that the future determines the present. They are not incorrect, because God sees all and knows all, including the future.
Pentacostalism is all about end time prophecies in the Bible as they interpret them. You cannot attend a service without the book of Revelation being brought up and they've published miles of literature about that very subject including a popular book series. The anti-christ, the mark of the beast, the rapture are all part and parcel of Pentecostalism.
Pentecostalism is not linked to eschatology in any way. Some people think the two are related in a more remote way, but that is not the case. The views of the beliefs have too many differing views that are basic to each principles. These to believes should not be linked in any way.
Yes, it is a fact that Pentecostalism is linked to eschatology. But this doesn't just stop at Pentecostalism; rather, you can insert any other religion, sect, or cult in the place of Pentecostalism and ask the same exact question. This is how it's been for thousands of years, quite obviously.
The general definition of eschatology is a belief concerning death, the end of the world, or the ultimate destiny of humankind. Pentecostalism is a movement within Christianity that focuses on a persons direct experience of God through Baptism. Pentecostal followers also believe that the Second Coming could happen at any time so being ready is of utmost importance but this is found in many branches of Christianity so I do not believe they are inextricably linked.