The very dust and silence in here seemed to tingle with some secret magic.

The word very is a key part of this sentence, which essentially says,

There was so much magic in here, even the dust and the silence seemed to tingle with magic.

[Collins][1] lists, among its definitions of very:

used in metaphors to emphasize the applicability of the image to the situation described

In other words, getting back to your intitial question, no, inanimate objects don't usually "tingle" with magic, but this room is so enchanted, that these very ordinary things (dust and silence) seemed to tingle with magic. The fact that the verb tingled is being applied in such an "unusual" way is not a mistake; in fact, it is quite intentional, because it helps the reader picture a room that has an aura of enchantment and wonder.

Also, it's worth noting the significance of the word seemed. When included in a sentence, seem can help stretch the applicability of a verb beyond its normal limits.

The weather was so nice, even the clouds seemed to sing.
The haunted house was so isolated, even its empty rooms seemed to urge us away.

although, when speaking figuratively and metaphorically, words such as very and seemed aren't required, because they can be inferred from the context:

I was so hungry, I could hear the pastries screaming my name.

which doesn't mean I was hallucinating, it simply means:

I was so hungry, it seemed like the very pastries were screaming my name. [1]: http://www.collinsdictionary.com/dictionary/english/very

The very dust and silence in here seemed to tingle with some secret magic.

The word very is a key part of this sentence, which essentially says,

There was so much magic in here, even the dust and the silence seemed to tingle with magic.

Collins lists, among its definitions of very:

used in metaphors to emphasize the applicability of the image to the situation described

In other words, getting back to your intitial question, no, inanimate objects don't usually "tingle" with magic, but this room is so enchanted, that these very ordinary things (dust and silence) seemed to tingle with magic. The fact that the verb tingled is being applied in such an "unusual" way is not a mistake; in fact, it is quite intentional, because it helps the reader picture a room that has an aura of enchantment and wonder.

Also, it's worth noting the significance of the word seemed. When included in a sentence, seem can help stretch the applicability of a verb beyond its normal limits.

The weather was so nice, even the clouds seemed to sing.
The haunted house was so isolated, even its empty rooms seemed to urge us away.

although, when speaking figuratively and metaphorically, words such as very and seemed aren't required, because they can be inferred from the context:

I was so hungry, I could hear the pastries screaming my name.

which doesn't mean I was hallucinating, it simply means:

I was so hungry, it seemed like the very pastries were screaming my name.