My grammar book lists this grammar point as being more negative in connotation. Sure, surprising information can be negative, but that's not always the case!
According to my grammar book: 後ろの文に否定的、非難の内容がくることが多い。

it seems that the noun doesn't have to be a person - ex. 最近流行っている歌ときたら、心に残らないものばかりだ。

While trying to find any info on the ときている grammar, I found some dictionary entries for 来る that include ときたら together with alternate grammar forms, and also list emphasis as one of its meanings/usages. I'm not quite sure what needs to be added to this page, but I've included some relevant excerpts below from the dictionaries I looked at; I hope they're helpful.

goo辞書 definition 6
（「…ときたら」「…ときては」「…とくると」などの形で）ある物事を特に取り上げ強調して言う意を表す。特に…の場合は。…について言うと。「酒とくると、からっきしだめだ」「甘い物ときたら、目がない」

明鏡国語辞典 definition 18
＜「…とくると」「…ときては」「…ときたら」「…ときた日にゃ」などの形で＞相手の話題を見計らってこちらに引き取るといった気持ちで、物事を話題としてとりたてる。
「音楽とくるとやはりモーツァルトだね」「今時の大人ときたら全くしょうがないなあ」
［表現］「…ときたら」「…ときた日にゃ」には、多くあきれる気持ちなどがこもる。また、後者は俗語的な言い方。

新和英大辞典 definition 9
［そのことを強調する］
彼女は甘いものと来たら目がない。
She (just) can't control herself when it comes to sweets. | She has a real weakness for sweets.
あいつと来たら彼女に夢中でちっとも仕事をしない。
He's so 「crazy about [head and heels over] her that he's not getting any work done.
日本の夏は高温の上に多湿と来ている。
Not only are Japanese summers hot, they're extremely humid. | On top of all the heat, Japanese summers are (also) incredibly humid.
彼の会社は倒産したばかりなんだ。そこへ来て息子さんの交通事故だろ。彼相当まいってるよ。
His company has just gone bankrupt. Then on top of that comes his boy's traffic accident, right? Oh, he's really feeling depressed.

I think that's a good idea for the definition. But I'm kinda confused about the とくると and ときては forms. They don't appear in my grammar dictionaries with ときたら but they seem to be consistently grouped together with ときたら in vocab dictionaries. Do they have the same meaning/usage as ときたら, or is there some subtle difference?

Wondering if @mysticfive has any information on the topic.