Tithe Taker does not increase cost of cycling
Tithe Taker does not increase the cycling cost for my opponent during my turn.
Immolation Shaman and Tithe Taker aren't the same at all.
Immolation Shaman's ability applies to "abilit[ies] of an artifact, creature, or land". Cards in hand or in a graveyard aren't artifacts, creatures or lands, they're just cards, so the ability isn't triggered by cycling or by other abilities that are activated from the hand or graveyard.
Tithe Taker's ability applies to all activated abilities regardless of what kind of object their source is.
Whilst there is no mention on gatherer for Tithe Taker, looking up gatherer for Immolation Shaman (which has a similar ability) states otherwise.
25/01/2019 Immolation Shaman’s first ability doesn’t trigger when an opponent activates an ability of a card in hand (such as cycling) or a card in a graveyard (such as that of Bone Dragon), even if that causes a card to be put onto the battlefield.
I would expect the same ruling to apply to Tithe taker, and thus it should also be added to gatherer for Tithe Taker.
Rules for cycling
702.28a Cycling is an activated ability that functions only while the card with cycling is in a player’s hand. “Cycling [cost]” means “[Cost], Discard this card: Draw a card.”
Tithe taker should increase the cost of it during my turn