求教：Newly installed water heater and the venting issue

请原谅我用英文，因为感觉英文更容易描述我的问题。 

My old water heater is dead (leaking), got a new one (Rheem Performance Platinum 50 Gal) from Homedport and installed by their contractor.

After installation, the installer turned the heater on but found the heat backdrafts, which heat up the tank. He turned it off and told me the vent must be blocked by something and I need to find some chimney people to check the chimney. The Installer left with the heater off.

We live in very cold region. We thought it might be because the cold air stuck in the vent and heat from heater is not strong enough to push the cold air out. Talked with the installer about this possibility but he did not think so. 

After the installer left, as a test, I used my electric blanket to warm up the vent pipe. Then used lighter to check and see the fire went up or down. Once I saw the fire went up, I tunred on the water heater, the vent works very well. 

Now the problem is:

The company that scheduled the installation for us called me today and asked how everything is going with the water heater. I told the caller about the initial vent issue, how we solved it and now it works fine. Suprisingly, very soon after I hang up the phone, their "operation manager" called me and insisted that I need to find a professional chimney inpector to check the chimney, otherwise my warranty will be voided because I "did not follow installer's instruction to have the chimney checked". 

请教这里有经验的朋友:

1。这种情况我应该怎么办？必须得找人检查 chimney 吗？不检查的话，真的会void the warranty 吗?

2. Chimey Inspection 大概多少钱? 加clean up 另外再加钱吗？

3. water heater 的 venting pipe 和chimney 是一回事吗？检查chimney 的人，会帮你检查water heater的venting pipes 吗？

我家的 heating and fireplace are working fine。不过在冷天给fireplace生火的时候，有时候刚开始点火那会会有一点点烟倒灌，但等火燃起来就好了。这也是为什么我们会想到冷空气的原因。

不好意思，怕说不明白同时自己也确实不明白这些事情，所以写的有点长。诚请大家给提供点建议，非常感谢！